Unit3_bruns

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Simple Harmonic Motion oseillation: when there is a regular and repeating vibrations periodic vibration: Simple Harmonic motion (SHM)
 * simple harmonic oscillator
 * small initial angles only

Lab: Masses on Springs question: What is the relationship between the force that a spring exerts on a mass and the distance the spring stretches. hypothesis: I think that there is going to be a linear relationship. Data and Calculations: Questions: What is the meaning of the slope? The spring force constant Question:What is the relationship between the period of oscillation and the mass? data and calculations: analysis: The first graphs show a linear relationship. We can see the accuracy by looking at the R 2 value. Our accuracy was 99%. This shows that the change in force and the change in distance when putting on masses have linear relationships. The second graph shows the relationship between the period of the oscillation and the mass show a direct square root. This was also very accurate by having an R 2 value of 99%. Although, there were a couple of sources of error during these 2 experiments. First, when many people were taking time, the reaction times using a handheld stop watch varied between each person. Also, each person used a different spring, therefore showing that the springs are not identical and could vary the measurements from your lab. Lastly, the distance measurement were hard to do. It was complicated to measure how much farther the distance the spring stretches.
 * Part A:**
 * Part B:**

Waves- Basic properties and characteristics Lab: Slinkies!
 * **terms** || **definition** ||
 * waves || * electromagnetic
 * do not require medium
 * mechanical--require medium ||
 * medium || * the material that carries the wave made of interacting particles ||
 * transverse || * the particles perpendicular to the direction the wave travels
 * crest: max displacement
 * trough: minimum displacement ||
 * longitudinal || * the particles occillate parallel to the direction the wave travels
 * compression: high pressure particles are closer together
 * rose fraction:low pressure particles are spread out farther ||
 * amplitude || * from equilibrium to crest (or trough) ||
 * period || * time for one complete cycle (s) ||
 * wave speed || * v=d/t
 * v=wavelength/period ||
 * frequency || * how many waves pass in one second ||
 * reflection || * encounters an obstacle and bounces off of it
 * angle of incidence= angle of reflection
 * the nature of the boundary ||
 * boundary || * where medium changes ||
 * refraction || * encounters a boundary
 * changes direction when entering new medium due to change in wave speed
 * change in the direction of waves as they pass from one medium to another
 * **wave speed is completely dependent on what medium**
 * **when you do change media, speed will change BUT frequency remains constant** ||
 * diffraction || * encounters and obstance or an opening
 * the wave bends around and spreads to fill in the space behind
 * bending to fit through and opening
 * Diffraction shows a change in direction of waves as they pass through an opening or around a barrier in their path.
 * **bigger the opening, less diffraction, shorter the wavelength, less diffraction** ||
 * interference || * 2 waves traveling in the same medium are at the same place at the same time
 * their energies temporarily sum

**Procedure:****//Part I// – Marking the floor** **//Part II// – Making a transverse pulse** Homework 26 and 27 __**Vibrational motion**__ An example of vibrational motion is a bobble head. The resting position is the position assumed by the bobblehead when it is not vibrating which is also known as equilibrium position. If a force was applied, the equilibrium is unbalanced and therefore shows there is a force vibration because there is motion and unbalanced equilibrium. __**3 characteristics of a graph**__ There are 3 characteristics of the graph shape, periodic nature, and damping. The shape shows the shape of a sine wave. The position of the mass is a function of the sine of the time. The periodic nature shows basically a cycle of vibration showing the movement of the mass from its resting position to its maximum height, back down past its resting position, to its minimum position, and then back to its resting position. Finally, using the measurements from the time axis, you can find out the time of one complete cycle. Lastly, damping is when some energy is being dissipated over the course of time. __**Dominant forces**__ There are two dominant forces acting upon a pendulum during motion. There is the force of gravity that acts downward upon the bob. There is also the tension force resulting from the string pulling upon the //bob// of the pendulum always towards the pivot point. __**Wave**__ A wave is disturbance that travels through a medium from one location to another location. For example when a slinky is stretched from one location to another and is at rest, it is at rest position. Then moving the slinky and putting them at rest, is a disturbance. A pulse is a single disturbance moving through a medium from one location to another location. By doing this repeatedly represents a wave. __**Types of waves**__ There are transverse, longitudinal, surface, electromagnetic, and mechanical waves. Transverse waves are waves in which particles of the medium move in a direction perpendicular to the direction that the wave moves. Longitudinal waves are waves in which particles of the medium move in a direction parallel to the direction that the wave moves. Surface waves are waves in which particles of the medium undergo a circular motion. An electromagnetic wave is capable of transmitting its energy through a vacuum. Lastly, mechanical waves are not capable of transmitting its energy through a vacuum. __**Description of waves**__ There are many different ways to describe waves. For example, there is the crest where the wave is the point on the medium that shows maximum amount of positive or upward displacement from the rest position. The trough shows the maximum amount of negative or downward displacement from the rest position. The amplitude shows maximum amount of displacement of a particle on the medium from its rest position. Representing the wavelength shows the length of one complete wave cycle. __**Frequency**__ There are regions where a slinky becomes compressed, but also spread apart. Compression is the point on the medium where a longitudinal wave is traveling that has the maximum density. Rarefaction is the point on a medium where a longitudinal wave is traveling that has the minimum density.The frequency of a wave shows how often the particles of the medium vibrate when a wave passes through the medium. The unit for frequency is Hertz. To find the frequency, you must do **frequency= 1/period( also reciprocated for period)** The energy transported by a wave is directly proportional to the square of the amplitude of the wave. This is shown by E is proportional A 2 __**speed of wavelength**__ Since a wave is disturbance, one might want to know the speed of a wave. To find a speed of a wave you do Speed= distance/time. The speed of a wavelength would be represented like this **Speed = Wavelength • Frequency** __**reflected pulse**__ A reflected pulse is a disturbance that returns to the left after bouncing off the pole. The speed of the reflected pulse is the same as the speed of the incident pulse. The wavelength of the reflected pulse is the same as the wavelength of the incident pulse. The amplitude of the reflected pulse is less than the amplitude of the incident pulse. __**Transmitted pulse**__ The transmitted pulse (in the less dense medium) is traveling faster than the reflected pulse (in the more dense medium). The transmitted pulse (in the less dense medium) has a larger wavelength than the reflected pulse (in the more dense medium). The speed and the wavelength of the reflected pulse are the same as the speed and the wavelength of the incident pulse. __**Boundary behavior**__ The boundary behavior of waves: The wave speed is always greatest in the least dense rope. The wavelength is always greatest in the least dense rope. The frequency of a wave is not altered by crossing a boundary. The reflected pulse becomes inverted when a wave in a less dense rope is heading towards a boundary with a more dense rope. The amplitude of the incident pulse is always greater than the amplitude of the reflected pulse. The law of reflection is the waves will always reflect in such a way that the angle at which they approach the barrier equals the angle at which they reflect off the barrier. __**refraction of waves**__ The refraction of waves shows a change in the direction of waves as they pass from one medium to another. Diffraction shows a change in direction of waves as they pass through an opening or around a barrier in their path. [|vibration animation with word explanation and equations] [|Different types of wave motion] Lab: standing waves To determine the relationship between the number of harmonics, the frequency of the source, and the wavelength of transverse waves traveling in a stretched string. Electrically driven oscillator; pulley & table clamp assembly; weight holder & selection of slotted masses; black Dacron string;
 * 1) Place strips of masking tape approximately .75m long on the floor at 0.0 m, 5.0 m and 10.0 m.
 * 2) **//Mark//** and **//label//** a heavy ink/pencil line in the **//center//** of the tape at 0m.
 * 3) Mark and label lines 10.0 cm, 20.0 cm and 30.0 cm to the **//left//** and **//right//** of your center mark on each.
 * 1) Stretch your spring between the 0.0 m and 5.0 m tape marks on the floor with the rope loops around your wrist being located about 0.5 m beyond the tape marks on the floor.
 * 2) Move your hand back and forth at right angles to the stretched spring until you can produce a pulse that travels down only one side of the spring (that is, the bump on the spring due to the pulse is only on the right or left side of the spring).
 * 3) Send a pulse down the spring that has an **amplitude** of **10.0 cm**. Have the third member of your group time the pulse as it travels from 0.0 m to 5.0 m.
 * 4) Repeat steps #8-11 for pulses having amplitudes of 20.0 cm and 30.0 cm.
 * 5) Repeat steps # 8-11 for 10-m distance.
 * Discussion Questions**
 * 1) How do the speeds of the waves compare for the 3 different amplitudes of the 5.0 meter distance? Looking at the 20 cm amplitude specifically, the speeds were pretty accurate for the slinky speed. It showed the accuracy because the speeds increased, yet some of the times were off, giving it some issue of accuracy. For the 30 cm, there was an outlier of .121 which could have effected the data. For 40cm, the data was all over the place. I think that the 5 m gave us a less accurate time, due to the reaction times of different students. For the snakey speed, the answers were more accurate but, each speed came up to be around the same average time.
 * 2) Did amplitude influence the speed of the waves for the 5.0 meter distance? For the slinky, i don't think the amplitude influenced the speed of the waves that much, only by about .01 or .02. For the snakey speed, the amplitude had no effect or little effect at all because the average times came out to be .50, .50, and .51.
 * 3) How do the speeds of the waves compare for the 3 different amplitudes of the 10.0 meter distance? In our specific data, they pretty much made a constant increase in time, with the increase of the 3 amplitudes. For the snakey speed, the average time also went up by about .05 or .06 which is pretty constant.
 * 4) Did amplitude influence the speed of the waves for the 10.0 meter distance? In the 10.0 meter distance, I think that the amplitude influenced the speed of the waves a little. For the slinky, the speeds differed between .10 and .15. For the snakey speed, the speeds differentiated by about .05 and .06.
 * 5) How do the speeds of the waves compare for the 5.0 meter and 10.0 meter distances? They are actually pretty close to each other. I feel as though the type of spring for the slinky doesn't really matter  because whether or not it was a different type of slinky, and a different distance, there couldn't have always been accurate time, or there could have been looking at our results.
 * 6) What changed when you measured the time for 10-m vs. the 5.0-m distance? Choose as many as apply.
 * The medium changed.
 * **The wavelength changed.**
 * **The speed changed.**
 * The frequency changed.
 * 1) How do the speeds of the waves compare for the 2 different types of springs? The slinky took a longer time for the wave to get to the other side. On the other hand, the snakey slinky with more rings got there faster than the normal slinky which was bigger and more far apart.
 * 2)  What are some differences between the longitudinal and the transverse wave? Longitudinal particles oscillate parallel to the direction the wave travels. There is compression: high pressure particles are closer together and rarefaction:low pressure particles are spread out farther. In transverse waves,the particles are perpendicular to the direction the wave travels. There is the crest which is max displacement and the trough which is minimum displacement.
 * Purpose: **
 * Materials: **
 * Procedure: **
 * 1) Set the frequency of the oscillator to zero. Set the amplitude to maximum.


 * 1) Measure the length L of the string.


 * 1) Dial up the frequency a little at a time until you acquire a standing wave. If you are careful, you should be able to get the fundamental. However, if you don’t, it’s okay… just record the correct number of antinodes along with the frequency.


 * 1) <span style="font-family: 'Century Schoolbook','serif';">Measure the wavelength.

<span style="font-family: 'Century Schoolbook','serif';">1. What is the name given to a point on a vibrating string at which the displacement is always zero? **Node.** <span style="font-family: 'Century Schoolbook','serif';">2. What is the name given to a point at which the displacement is always a maximum? **Anti-node** <span style="font-family: 'Century Schoolbook','serif';">3. How is the length of the string related to the wavelength for standing waves? **<span style="font-family: 'Century Schoolbook','serif';">L= n <span style="font-family: 'Times New Roman','serif';">λ <span style="font-family: 'Century Schoolbook','serif';">/2 ** <span style="font-family: 'Century Schoolbook','serif';">4. What is the longest possible wavelength for a standing wave in terms of the string length? **Two times the string length (2L)**
 * 1) <span style="font-family: 'Century Schoolbook','serif';">Repeat for at least 7 different harmonics. These do not have to be consecutive.
 * <span style="font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">Data and Calculations: **
 * <span style="font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">Discussion Questions: **
 * <span style="font-family: 'Century Schoolbook','serif';">5. Use your graph to find the frequency for n = 20. (Try it. Does it work?) **

<span style="font-family: 'Century Schoolbook','serif';">6. What is the relationship between the speed of the wave and the harmonic number? **It remains constant.**

<span style="font-family: 'Century Schoolbook','serif';">7. What is the relationship between the speed of the wave and the frequency? **There is a direct relationship.** <span style="font-family: 'Century Schoolbook','serif';">8. What is the relationship between the wavelength and the harmonic number? **There is an inverse square relationship.** <span style="font-family: 'Century Schoolbook','serif';">9. What is the relationship between the wavelength and the frequency? **There is an inverse relationship**

<span style="color: #ac00ff; display: block; font-family: 'Comic Sans MS',cursive; font-size: 180%; text-align: center;">Sound notes || minimum amplitude || maximum amplitude || pitch || what we hear perception of frequency human hearing: 20-20000Hz human voice: 85-1100 Hz ||
 * Term || Definition ||
 * resonance || when the natural frequency of an object is reinforced by an external object, causing a standing wave to form ||
 * standing waves || a pattern created by the interference of a wave due to resonance
 * node || place where the is destructive interference
 * antinode || constructive interference
 * loudness
 * sound travels faster in:
 * water: 1500 m/s
 * solids
 * air: 343 m/s
 * steel: 5000m/s

<span style="color: #2100ff; display: block; font-family: 'Comic Sans MS',cursive; font-size: 200%; text-align: center;">Doppler effect
 * when you start to move, more crests start to move together
 * higher frequency
 * change in frequency due to the moving of the source-WAVES CRUSHED TOGETHER, higher frequency.
 * equation:



coclia: the sound waves hit the bone and transfers the vibrations into the coclia so then you can hear

<span style="color: #00b4ff; display: block; font-family: 'Comic Sans MS',cursive; font-size: 180%; text-align: center;">Homework 28 and 29 __**traveling wave**__ A traveling wave is a distinct wave pattern in the form of a sine wave that travels through the medium. It moves in an uninterrupted fashion until it encounters another wave along the medium or a boundary.You can see them when they are not confined to a given space along the medium. Also, not observed in a cord, but they still travel through the cord. __**standing wave**__ A standing wave is vibrational pattern created within a medium when the vibrational frequency of the source causes reflected waves from one end of the medium to interfere with incident waves from the source. They are only created at specific frequencies of vibration, which are known as harmonic frequencies. An upward displaced pulse at one end will interfere in the exact middle of the snakey with a second upward displaced pulse introduced from the same end if the introduction of the second pulse is performed with perfect timing. The same thing happens with a downward displaced pulse. Nodes are the points that undergo the maximum displacement during each vibrational cycle of the standing wave. Anti nodes are the points that undergo minimum displacement during each vibrational cycle of the standing wave. __**Harmonics**__ Harmonics are only created at specific frequencies of vibration. The first harmonic has 2 nodes, and the second has 3 nodes, but if it is one node, it is fundamental. To find the harmonic number, you must do L= n(antinodes)/2 lambda. __**Mechanical wave**__ A sound wave also known as a mechanical wave, has a medium that carries the disturbance from one location to another. The medium is usually air, but it can be anything like water or steel. Also, there is an original source of the wave. Last, the wave can be transferred from one location to another by particle-to-particle interaction. – used with tuning fork __**Sound waves**__ Sound waves in air are longitudinal because the particles of the medium through which the sound is transported vibrate parallel to the direction that the sound wave moves. __**Pressure wave**__ A pressure wave is a repeating pattern of high-pressure and low-pressure regions moving through a medium. The fluctuations in pressure shown by the detector occur at periodic and regular time intervals __**Frequency**__ Frequency is how often the particles of the medium vibrate when a wave passes through the medium. The frequency wave is measured as the number of complete back-and-forth vibrations of a particle of the medium per unit of time. 1 hertz= 1 vibration/second The sensation of frequency is known as the pitch. A high pitch sound corresponds to a high frequency sound wave and a low pitch sound corresponds to a low frequency sound wave. __**Intensity**__ Intensity is the amount of energy that is transported past a given area of the medium per unit of time. The equation to measure intensity is intensity=energy/time*area OR intensity=power/area. Units are watts/m2 __**Wave interference**__ Wave interference is the phenomenon that occurs when two waves meet while traveling along the same medium. Constructive interference is if two upward displaced pulses having the same shape meet up with one another while traveling in opposite directions along a medium, the medium will take on the shape of an upward displaced pulse with twice the amplitude of the two interfering pulses. destructive interference - opposite __**Beats**__ Beats are the periodic and repeating fluctuations heard in the intensity of a sound when two sound waves of very similar frequencies interfere with one another. Relating to frequency, it shows the high to low volume. __**Doppler effect**__ The Doppler effect is the effect produced by a moving source of waves in which there is an apparent upward shift in frequency for the observer and the source are approaching and an apparent downward shift in frequency when the observer and the source is receding. __**boundary behavior**__ The behavior of a wave reaching the end of the medium is known as boundary behavior. There are 4 types: reflection, diffraction, transmission, refraction. When it reaches the end of the medium, there is a reflected pulse. Lastly, a portion of energy is transmitted into the new medium. [|Standing Waves video] [|Doppler Effect video] [|Sound properties video]

<span style="color: #ff00e3; display: block; font-family: 'Comic Sans MS',cursive; font-size: 170%; text-align: center;">More Sound Notes Intensity
 * How much power a sound source emits
 * Related to the rate of energy used to create sound and distance from the source
 * Quantitative measurement of loudness
 * Symbol I= Power(w/t)/surface area (4(pi)r2
 * Units- watts/m2
 * Inverse square relationship
 * Also related to amplitude
 * Every source is surrounded by a bubble of sound- sphere, traveling outward at constant speed
 * When you emit 100w
 * Why is there less sound when it needs to go farther away the energy is dissipating
 * Decibels
 * Intensity level
 * Sound level
 * Deci- a logarithmic scale
 * Name || Intensity w/m2 || intensity level (dB) ||
 * Jet plane at 50 m || 100 || 140 ||
 * threshold of pain || 10 || 130 ||
 * threshold of discomfort || 1 || 120 ||
 * siren || 1 x 10 -2 || 100 ||
 * diesel truck || 1 x 10 -3 || 90 ||
 * talking || 3 x 10 -6 || 65 ||
 * whisper || 1 x 10 -10 || 20 ||
 * threshold of hearing || 1 x 10 -12 || 0 ||

<span style="color: #00b4ff; display: block; font-family: 'Comic Sans MS',cursive; font-size: 170%; text-align: center;">Lab: Resonance Tubes ** Objective: ** What is the relationship between the length of a tube and its resonant frequencies? **Hypothesis:** I think the relationship is that the length of the tube if it is longer, the frequency is going to be harder to stay at the resonant frequency and lower ** Materials: ** Resonance tubes with length scale marked on the tube, audio generator, speaker, class thermometer. ** Experimental Procedure: ** **// Part A: Closed Tube //** <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 16px; text-align: left;">1) Measure the room temperature of the air and record it in Data Table 1. If the thermometer in the room measures temperature in oF it is necessary to convert to oC. <span style="display: block; font-family: 'Times New Roman',Times,serif; text-align: left;"> 2) Your teacher will assign you a frequency, between 300 and 800 Hz. Calculate the wavelength of this sound, using the speed from Step 1. <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 16px; text-align: left;">3) Calculate the theoretical length of the column of air in the closed tube of the first 5 harmonics. Circle the ones between 0 and 2.6 meters. <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 16px; text-align: left;">4) Set the audio generator to emit the frequency that has been assigned to you. Lower the volume (amplitude) so that it is just barely audible. <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 16px; text-align: left;">5) Set the speaker next to the open end of the resonance tube. Set the tube to the first calculated length. Adjust the length of the tube by moving the inner tube in small increments in or out, until you hear the sound at its maximum amplification. Record the adjusted lengths as the Measured. <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 16px; text-align: left;">6) Repeat the procedure for the other calculated lengths. **Calculations: Closed tube**
 * Finding
 * B= 10(log)(I/1o - 1 x 10 -12 ) [[image:naaah.JPG width="432" height="293"]]

**// Part B: Open Tube //** <span style="display: block; font-family: 'Times New Roman',Times,serif; text-align: left;"> 1) Your teacher will assign you a frequency, between 300 and 800 Hz. Calculate the wavelength of this sound, using the speed from Step 1. <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 16px; text-align: left;">2) Calculate the theoretical length of the column of air in the open tube of the first 5 harmonics. Circle the ones between 1.3 and 2.6 meters. These are the harmonics that you will try to hear experimentally. NOTE: You cannot test lengths SMALLER than 1.3 m or BIGGER than 2.6 m. Caluclate bigger harmonics to substitute for those values less than 1.3 m. <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 16px; text-align: left;">3) Set the audio generator to emit the frequency that has been assigned to you. Lower the volume (amplitude) so that it is just barely audible. <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 16px; text-align: left;">4) Set the speaker next to the open end of the resonance tube. Set the tube to the first calculated length. Adjust the length of the tube by moving the inner tube in small increments in or out, until you hear the sound at its maximum amplification. Record the adjusted lengths as the Measured. <span style="display: block; font-family: 'Times New Roman',Times,serif; font-size: 16px; text-align: left;">5) Repeat the procedure for the other calculated lengths **<span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;"> Calculations: Part B **  **Graph:Data**  **<span style="font-family: 'Times-Roman','serif'; font-size: 16px;">Discussion Questions: ** >>
 * <span style="color: #ff0000; font-family: 'Times New Roman',Times,serif; font-size: 16px;">**For an ideal resonance tube, an antinode occurs at the open end of the tube. What characteristic of real resonance tubes slightly alters the position of this antinode?**
 * <span style="color: #ff0000; font-family: 'Times New Roman',Times,serif; font-size: 16px;">A .8 shift for a closed resonance tube and .4 of a shift for an open resonance tube slightly alter the position of the antinodes
 * <span style="color: #ff0000; font-family: 'Times New Roman',Times,serif; font-size: 16px;">**Why must there be an antinode at the end of the resonance tubes?**
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">There is some chaos at the ends that shift the position and makes it off a bit. If a node was closed off, then there wouldn't be a sound produced out of the outside. You have to use an antinode because then you will get a sound produced.
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">How long would the closed tube have to be to get the 11th harmonic? **
 * <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 16px;">length of closed tube= slop x harmonic
 * <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 16px;">.1253*11
 * <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 16px;">1.3783
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">How long would the open tube have to be to get the 10th harmonic? **
 * <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 16px;">Length of the open tube=slope x harmonic
 * .2531*10
 * 2.531 meters
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">Draw a figure showing the fifth resonance in a tube //closed// at one end. Show also how the length of the tube L5,is related to the wavelength, λ. **
 * <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 16px;">l(
 * <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 16px;">This figure shows the 5th resonance tube with one end closed. This shows that there is a 5/4 wavelengths showing that the length of the tube= 5/4lambda
 * **<span style="font-family: 'Times New Roman',Times,serif; font-size: 16px;">Draw a figure showing the fifth resonance in an //open// tube. Show also how the length of the tube L5,is related to the wavelength, λ. **
 * <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 16px;">)(
 * <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 16px;">This figure shows 5 half waves which shows that there are 5/2 wavelengths in the open tube, showing that the length of the tube= 5/2 lambda

<span style="color: #00ff00; display: block; font-family: 'Comic Sans MS',cursive; font-size: 190%; text-align: center;">Properties of Sound
 * Name || Explanation ||
 * reflection || * echo (<17)
 * reverberation ||
 * refraction || * [[image:cold.JPG]] ||
 * diffraction || * spreads around the barrier
 * [[image:circls.JPG]] ||
 * interference || * beats
 * resonance in strings and tubes ||

<span style="color: #00ffae; display: block; font-family: 'Comic Sans MS',cursive; font-size: 190%; text-align: center;">Homework 30 and 31 __**Natural frequency**__ Natural frequency is when an object tends to vibrate when hit, struck, plucked, strummed or somehow disturbed. If the amplitude is high enough, the vibrating sound will produce audible waves. __**Resonance**__ Resonance is when two interconnected objects share the same vibrational frequency (such as tuning forks). When one of the objects is vibrating, it forces the other object to go into vibrational motion creating a large vibration. If there is a sound wave that is in the audible range of human beings hearing, a loud sound should be hear. __**Harmonics, Antinodal,, Nodal**__ Specific frequencies of vibration are known as harmonics. At any other frequency (not in harmonic) an interference of reflected and incident waves result in a disturbance of the medium that is irregular and non-repeating. By points that appear by standing still show a standing wave pattern. Nodal points are known as the points standing still. Antinodal points create a pattern of nodal and antinodal points. __**First harmonic**__ The first harmonic is the lowest frequency produced by any particular instrument. This is shown with 2 nodes and one antinode. For the second harmonic, it has one more node. Note: the ends are also considered nodes. The third harmonic shows adding 2 more nodes. __**Resonance**__ Resonance is when one object vibrating at the same natural frequency of a second object forces that second object into vibrational motion. The result of resonance is always a big vibration and a loud sound. __**Open end column**__ An open end column is if both ends of the tube are uncovered or open. For example, the flute and the recorder. The distance between antinodes on a standing wave pattern= one-half of a wavelength. __**Closed end column**__ A closed end column is when one end is open for the sound waves and one end is closed. The distance between adjacent antinodes on a standing wave pattern is equivalent to one-half of a wavelength. Vibrational nodes will be present at any closed end.

[|Resonance and Standing Waves]



<span style="color: #ebb52b; display: block; font-family: 'Comic Sans MS',cursive; font-size: 180%; text-align: center;">Light basics
 * electromagnetic- can travel through a vacuum
 * source: accelerating charged particle (emitted by all sorts of places, stars mainly)
 * emit electromagnetic wave
 * 3-D
 * magnetic component
 * source is accelerrating, charged particle
 * no medium required
 * speed of light c=3 x 10 8
 * always travels in a straight line, unless caused to do otherwise- **linear propagation**
 * linear
 * <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 16px;"> How is the diagram to the right organized? What information is provided?
 * <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 16px;">Order of wavelength
 * <span style="font-family: 'Times New Roman',Times,serif;">Radio waves have big wavelength, gamma rays- smaller wavelength
 * <span style="font-family: 'Times New Roman',Times,serif;"> Small to big frequency
 * <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 16px;">What is the relationship between energy and frequency?
 * <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 16px;"> Energy is due to its frequency
 * <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 16px;">Which EM Wave has the highest energy? Lowest?
 * <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 16px;">gamma, radio
 * infared
 * heat
 * microwave
 * boil water
 * radio
 * low frequency
 * visible light
 * ROY G BIV
 * change density, changes wave speed
 * optical density
 * how well visible light can travel through the medium
 * more optically dense, the slower the light goes
 * transparent
 * gets remitted in the same direction that it is going absorbs, jiggles and re emitts
 * transluscent
 * atom takes in electromagnetic radiation, jiggles, then re emitts it in a direction
 * ROY G BIV
 * red- low frequency, big wavelength
 * violet- high frequency, small
 * What is the relationship between EM wave speed and the medium?
 * The more optically dense, the slower it is
 * What happens to the EM frequency when the wave speed changes?
 * When you change media, frequency stays the same
 * What happens to the EM wavelength when the wave speed change?
 * It has to go down
 * What is the relationship between EM wavelength and color-perception?
 * Losing wavelengths, colors will shift

<span style="color: #ffee00; display: block; font-family: 'Comic Sans MS',cursive; font-size: 180%; text-align: center;">Light **1 slit** **2 slits**
 * particle vs wave
 * corpuscular
 * "optiks"
 * wave
 * Thomas Young
 * 2 slits with a screen
 * the 2 slits show lines with bright and dark colors - WAVES NOT DOTS
 * called wavelengths
 * einstein
 * photoelectric effect
 * influenced the result of the experiment
 * Huygens
 * measuring eclipses
 * light has a finite speed
 * 2 x 10 8 m/s
 * fizeau
 * toothes source
 * light source
 * could view through the teeth--d--mirror
 * ~3 x 10 8
 * light bends around an obstacle or through an opening which creates an interference pattern
 * wavelength mus be on the same order of magnitude as the opening/obstacle
 * less diffraction as opening decreases in size
 * pattern will be closer together
 * central antinode is very bright (2x), double width,
 * fringe is the pattern to the right and left of central antinode
 * combination of interference and diffraction
 * distance between slits increases get closer pattern
 * central antinode is same width and same longitude as fringe
 * looks similar to diffraction
 * diffraction grating has hundreds or thousands of slits per mm as wavelength decreases,

<span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 180%; text-align: center;">Image Characteristics upright =distance virtual laterally inverted ||  || upright virtual located behind the mirror ||  || upside down-invertedCurve when you get closer- right side up || * upright
 * Type || definition || Image characteristics || Orientation || Size || * light is actually at the position it seems to be
 * can be **PROJECTED** ||  || virtual || * light is NOT really where it seems to be
 * **illusion- CANNOT BE PROJECTED** ||  || orientation ||   ||   || size || * enlarged
 * unchanged
 * reduced ||  ||   ||
 * plane || flat || same size
 * diverging || convex in shape || reduced
 * converging || concave in shape || real
 * inverted ||
 * relative to the optical plane and/or the focal point

all plane mirror normal- the line perpendicular to the surface specular reflection- surface is flat diffuse reflection- surface is irregular
 * virtual image
 * upright
 * same size
 * located in side mirror- the same distance

<span style="color: #006cb0; display: block; font-family: 'Comic Sans MS',cursive; font-size: 20.8px; text-align: center;">Lab: Reflection Plane mirror <span style="color: #ff0044; font-family: 'Times New Roman',Times,serif; font-size: 90%;">**Objectives:** Demonstrate that reflection from a plane source the angle of incidence is equal to the angle of reflection. <span style="color: #ff0044; font-family: 'Times New Roman',Times,serif; font-size: 90%;">**Materials:** Optical Bench, Light source, circular reflecting surface, protractor, straight edge, compass, pencil, black tape, white and/or tracing paper. <span style="color: #ff0044; font-family: 'Times New Roman',Times,serif; font-size: 90%;">**Theory:** <span style="color: #ff0044; font-family: 'Times New Roman',Times,serif; font-size: 90%;">**Reflection** <span style="color: #ff0044; font-family: 'Times New Roman',Times,serif; font-size: 90%;">The reflection of light from a plane surface is described by the law of reflection, which states that the angle of incidence, θi, is equal to the angle of reflection, θr, as can be derived by Fermat’s Principle. By convention, these angles are measured with respect to a line perpendicular to the plane surface. Reflection from a plane mirror or a flat transparent plane surface of a piece of glass or plastic are the most easily demonstrated examples of the law of reflection.

<span style="color: #ff0044; font-family: 'Times New Roman',Times,serif; font-size: 90%;">In Figure 1(a) several rays are shown incident on a plane surface, and in each case the reflected ray is also shown. For each ray, the angle of incidence θi is seen to be equal to the angle of reflection θr. <span style="color: #ff0044; font-family: 'Times New Roman',Times,serif; font-size: 90%;">**Procedure** <span style="color: #ff0044; font-family: 'Times New Roman',Times,serif; font-size: 90%;">**Part A: Reflection** <span style="color: #404040; font-family: 'Times New Roman',Times,serif;">Analysis <span style="color: #ff0044; font-family: 'Times New Roman',Times,serif; font-size: 16px;">Calculate the difference (|θreflected//–// θincident|) between the measured values of the incident angle and the reflected angle for each of the three rays and record them in the Calculations Table. Analysis Questions: > ,
 * 1) <span style="color: #ff0044; font-family: 'Times New Roman',Times,serif; font-size: 90%;">Place the ray box, label side up, on the guidesheet on this back of this paper. Adjust the light box so that only one beam of light exits the box. Line this up along the 10˚ line.
 * 2) <span style="color: #ff0044; font-family: 'Times New Roman',Times,serif; font-size: 90%;">Set the mirror so that its back is on the line.
 * 3) <span style="color: #ff0044; font-family: 'Times New Roman',Times,serif; font-size: 90%;">Trace the angle of reflection lightly, by making a few dots.
 * 4) <span style="color: #ff0044; font-family: 'Times New Roman',Times,serif; font-size: 90%;">Repeat for each angle of incidence.
 * 5) <span style="color: #ff0044; font-family: 'Times New Roman',Times,serif; font-size: 90%;">Extend all of the lines showing the ray directions until they intersect at one point. Using a protractor, measure the reflected angles θ//1r//, θ//2r//, θ//3//etc, for each of the rays. Record all these angles (to the nearest 0.1o) in the Data Table.
 * 6) <span style="color: #ff0044; font-family: 'Times New Roman',Times,serif; font-size: 90%;">MY drawing:
 * 1) <span style="color: #ff0052; font-family: 'Times New Roman',Times,serif; font-size: 16px;">Are your data consistent with the law of reflection? State your answer as quantitatively as possible. My data is consistent with the law of reflection because the law of reflection states  <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 14.4px;">that the angle of incidence, θi, is equal to the angle of reflection, θr. In my data, I barely had any error. For example, when i look at the angle of incidence in trial 3 when it was 8 degrees, the angle of reflection was the same, giving me a percent error of zero. However there could be a little human error because in trial 1, the angle of incidence was 23, and the angle of reflection was 22, shows that there could have been a human error while measuring the angles.
 * 2) <span style="color: #ff0052; font-family: 'Times New Roman',Times,serif; font-size: 16px;">Where is the image in a plane mirror located? <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 16px;">The image in the plane mirror is located behind the glass.
 * 3) <span style="color: #ff0052; font-family: 'Times New Roman',Times,serif; font-size: 16px;">If you were required to graph the angle of incidence vs. the angle of reflection, what would be the shape of the graph? <span style="color: #000000; font-family: 'Times New Roman',Times,serif; font-size: 16px;">What would the slope of the line be? the shape of the graph would be a straight line. This is due to the slope being one since the angle of incidence and the angle of reflection are equ al.
 * 4) <span style="color: #ff0052; font-family: 'Times New Roman',Times,serif; font-size: 16px;">What are the characteristics of all images from plane mirrors? There are 4 components to the characteristics of all images in plane mirrors. First, the images are virtual. They are also laterally inverted. The image is the same size as the object. And lastly, the image is at the same distance from the mirror as the object is from the mirror

<span style="color: #00ff6b; display: block; font-family: 'Comic Sans MS',cursive; font-size: 28.8px; text-align: center;">Curved Mirrors point a: vertex- principle axis hits the mirror(optical plane) point c: center of curvature r: distance from the optical plane to the vertex F= focal point f= distance from focal point to vertex: focal length focal length= half the radius of curvature <span style="display: block; font-family: 'Comic Sans MS',cursive; font-size: 180%; text-align: center;">Lab: Reflection in curved mirrors ** Objectives: ** Demonstrate the focal properties of spherical reflecting surfaces.

** Materials: ** Optical Bench, Light source, circular reflecting surface, protractor, straight edge, compass, pencil, black tape, white and/or tracing paper. ** Theory ** ** Focal Properties of Mirrors ** Descriptions of the focal properties of reflection from spherical mirrors are shown in Figure 2. When parallel rays are incident on a concave spherical surface, reflected rays are converging and come to an approximate point focus. If //R// is the radius of curvature of the spherical surface, the focal point is a distance //f// from the vertex of the spherical mirror, where //f = R/2//. The distance //f// is called the “focal length” of the mirror and is positive by convention for a concave converging mirror. The reflection of parallel rays incident on a convex spherical mirror are diverging, but they appear to have come from a single point. The distance from the vertex of the mirror to that point is called the “focal length,” and its magnitude is given by //f = R/2//. By convention, the focal length is negative for a convex diverging mirror. ** Procedure **
 * 1) Slide the screen on the ray box so that five rays are produced.
 * 2) Put this lab sheet on the table. Set up the light source on top of it, so that there are 5 individual rays of light projected in the space below, with the middle ray on the solid line in the box.
 * 3) Put the **//concave//** mirror in front of the rays, adjusting it until you can see the convergence of the reflected rays meet somewhere on the solid line. Trace the mirror front, and the incident and reflected rays on the paper, by making a couple of dots and connect them with a ruler after removing the mirror.
 * 4) The point of convergence is the focal point. Label the focal point, focal length, center of curvature, and radius of curvature clearly on your diagram.
 * 5) Measure the focal length of the concave reflector. Record it in the Data Table as //fcon//.
 * Analysis Questions**
 * 1) ** How does the measurement of the focal point found for the convex mirror relate to the focal point found for the concave mirror? **
 * 2) ** How well did your image characteristics agree with the predicted descriptions? **
 * 3) ** Why were you not asked to determine whether the images were real or virtual? **

<span style="color: #00ffae; display: block; font-family: 'Comic Sans MS',cursive; font-size: 180%; text-align: center;">Refraction:
 * Shorter wavelengths are influence less by the prism

<span style="color: #ff0000; display: block; font-family: 'Comic Sans MS',cursive; font-size: 180%; text-align: center;">Lab: Refraction **Purpose** To use Snell’s Law to determine the index of refraction of the acrylic Prism. **Equipment** Ray box, Prism, Protractor, White paper **Theory** According to Snell’s Law, n1sin q 1= n2sin q 2, where q 1 is the angle of incidence, q 2 is the angle of refraction, and n1 and n2 are the respective indices of refraction of the materials. The angle of refraction depends on the angle of incidence and the index of refraction of the material. See Figure 2.1. Because the index of refraction for light varies with the frequency of the light, white light which enters the material at a given angle of incidence will separate out into its component colors as each frequency is bent a different amount. The Prism is made of Acrylic, which has an index of refraction of 1.497 for light of wavelength 486 nm in a vacuum, 1.491 for wavelength 589 nm, and 1.489 for wavelength 651 nm (red). Notice that in general for visible light, the index of refraction for Acrylic increases with increasing frequency. **Procedure****Snell’s Law** **Calculations** **Analysis Questions** 1) How does the angle of incidence compare to the angle of refraction when light travels from a medium of low optical density (air) to a medium of high optical density (acrylic)?  2) How does the angle of incidence compare to the angle of refraction when light travels from a medium of high optical density (acrylic) to a medium of lower optical density (air)? 3) What would happen to a light that entered the acrylic along the normal? 4) Discuss how the angle of refraction changed with the angle of incidence. As the angle of incidence increased, the angle of refraction
 * dispersion: wave lengths disperse when it passes the prism, but to us it appears as one line
 * red bends less, violet bends the most
 * the hotter it is, the faster the wave can travel
 * behaves like a different medium
 * 1) Place the Prism on a sheet of paper and draw a sharp pencil line around it. Make a dark dot somewhere on the square edge. Use a protractor to measure 90 ° from the surface at that point; this will be your normal to the incident ray.
 * 2) Use the protractor to measure angles in 10 ° increments from the normal down to the block’s surface. These will be your incident rays.
 * 3) Place the ray box, label side up, on a white sheet of paper on the table. Adjust the light box so that only one beam of light exits the box. Line this up along the 10˚ line.
 * 4) Place the Prism on the table and position it so the ray passes through the parallel sides as shown in Figure 4.2.
 * 5) Make 1 dark mark on the light beam exactly where it exits the far side of the glass. Make a second mark somewhere else on this light beam. Use a ruler to connect these marks.
 * 6) Remove the Prism and on the paper draw a line connecting the points where the ray entered and left the Prism.
 * 7) Measure the angle of incidence ( q 1) and the angle of refraction ( q 2)with a protractor. Both these angles should be measured from the normal.
 * 8) Repeat the above for the remaining angles.
 * Make a graph of sin θi vs sin θr.
 * Use your graph of sin θi vs sin θr to find the equation of the line. Record this equation and the correlation coefficient.
 * Show why the slope of the line is the index of refraction of acrylic. Start with Snell’s Law, rearranging it to get it in the form of //sin θi vs sin θr//. (Remember that graph titles are //y// vs. //x//.)
 * If the index of refraction of acrylic is actually 1.50, what is the percent error? (If it is greater than 10%, you need to redo your data collection!)
 * 1) Choose one: always smaller, **always bigger**, or always constant.
 * 2) Provide evidence from the lab: **In this lab the angle of refraction when light travels from a medium of low optical density to a medium of high optical densoty, the angle of incidence was always higher. for example, when the angle of incident was 10, the angle of refraction was 5. if you look at the next the angle of incidence is 20 and the angle of refraction is 10. This shows that the angle of incidence is always greater.**
 * 1) Choose one: **always smaller**, always bigger, or always constant.
 * 2) Provide evidence from the lab: **the angle of refraction would be smaller because when you look at the 2 optical density's, acrylic and air, air can travel faster because it is less dense than the acrylic blocks that we used. the light tended to bend away from the normal when it had a higher optical density.**
 * 1) The light refracted towards the normal.
 * 2) The light refracted away from the normal.
 * 3) The light only reflected off the plate.
 * 4) ** The light did not refract, but went straight. **
 * 1) ** Increased. **
 * 2) Decreased.
 * 3) Remained the same.

<span style="color: #ff0052; display: block; font-family: 'Comic Sans MS',cursive; font-size: 180%; text-align: center;">Lesson 32: There are 3 waves of nature: reflection, refraction, diffraction. Waves reflect and bounce of an obstacle. What is important to remember is the angle at which the wave approaches a flat reflecting surface= the angle at which the wave leaves the surface. All waves undergo refraction which is the direction that the wavefront is moving undergoes a sudden change. The pathway that the wave is going is then bent. Diffraction involves a change in the waves direction when they pass an obstacle in their path.

A two point source interference pattern always has a nodal and antinodal pattern. The change in wavelength alters the number of lines in a pattern. An increase in frequency shows more lines per centimeter and a smaller distance between each consecutive line. A decrease in frequency shows fewer lines per centimeter and a greater distance between each consecutive line.

Polarized light waves are where the vibrations occur in a single plane. Polarization is the process of transforming unpolarized light into polarized light. An order number is a number assigned each line in the pattern of numbering the wave system. Nodal lines are assigned half numbers. Antinodal are assigned whole numbers like 1, 2, and 3 for the antinodal lines.

Path difference is the distance traveled by the two waves from their respective sources to a given point on the pattern. To calculate this you must do: PD = | S1A - S2A | = | 5 - 6 | = 1. To find the antinodal points PD= m x wavelength by 1’s, for nodal points PD= same but increments of .5

Youngs equation is = y • d / (m • L). This is able to show the wavelength on a nodal and antinodal line (order value). From this you can also find the distance between the slits or sources of the two light waves, the perpendicular distance from the point P to a point on the central antinodal line and the distance from point P to the sources.

[|Young's Experiment video]

<span style="background-color: #ffffff; color: #00ffae; display: block; font-family: 'Comic Sans MS',cursive; font-size: 180%; text-align: center;">Lesson 33: __**Luminous and illuminous objects**__ Luminous objects make their own light. Illuminated objects that reflect light to our eyes. If we didn’t have luminous objects, the illuminated objects would not be seen. When the sun disappears, and it starts to become dark, it shows the illuminated objects harder to see and appear black. __**Line of sight**__ The line of sight is when you want to view an object, you must look at the line of the object. When you look at the line of the object, and you find the line of the object and light will come from that object to your eye and you will be able to see along the line of sight. __**Ray of light**__ The ray of light is known as an incident ray. If the incident ray is reflected off of a mirror, that is known as the reflected ray. This shows that the object distance= image distance. This relates to the law of reflection because the angle of incidence= the angle of reflection. __**Specular vs diffuse**__ Specular reflection is when a reflection is reflected off of a smooth surface like a mirror. Diffuse reflection is when there is a reflection off of rough surfaces such as clothes or asphalt roadways. For example, and bumpy asphalt surface is better to drive on at night then a specular reflection road that has a lot of reflections off of the smooth surface on the ground. __**Finding an image**__ You can find the image location when observers are viewing the position of the object. When you find the image location, it is the image behind the mirror where all the light diverges from. __**Characteristics of images**__ A virtual image is an image where light does not actually reach. A real image is displayed through a curved mirror. When you look in the mirror and you raise your left hand, your right shows up. That is known as a left right reversal. The image is upright and isn’t inverted. To determine where the image is seen, you make a ray diagram. A ray diagram shows the path that light takes in order to view a point on the image of the object. [|Image formations in plane mirrors] [|Specular and Diffuse reflection] <span style="color: #ffb100; display: block; font-family: 'Comic Sans MS',cursive; font-size: 180%; text-align: center;">Lesson 34: __**Curved mirror:**__ Principle axis- a line passing through the center of the mirror Center of curvature- the point in the center of a sphere from which the mirror was sliced Vertex- the point where the principle axis meets the mirror Focal point- midway between the vertex and the center of curvature Radius of curvature- distance from the vertex to the center of curvature Focal length- the distance from the mirror to the focal point

There are 2 rules of reflection about concave mirrors. First, any incident ray traveling parallel to the principal axis on the way to the mirror, will pass through the focal point when it reflects. Second, any incident ray passing through the focal point on the way to the mirror will travel parallel to the principal axis when it reflects.

When the object is beyond C, located at C and located between C and F this creates real images. Although, concave mirrors can produce real and virtual images. In this situation, a virtual image is formed when the object is located less than one focal length from the concave mirror.
 * the object is located beyond the center of curvature (C)
 * Inverted
 * Reduced
 * Less than 1
 * Real
 * the object is located at the center of curvature (C)
 * Inverted
 * Stays the same
 * converge
 * the object is located between the center of curvature (C) and the focal point (F)
 * inverted
 * real
 * enlarged
 * converging
 * the object is located at the focal point (F)
 * NO IMAGE FORMED
 * the object is located in front of the focal point (F)
 * Upright
 * Enlarged
 * Virtual
 * Diverging

The mirror and magnification equation: Distance of image 1/f=1/di + 1/d0 Height of image hi/ho= - di/do

__**Convex mirrors**__ There are 2 rules to convex mirrors. First, any incident ray traveling parallel to the principal axis on the way to a convex mirror, will reflect that its extension will pass through the focal point. Second, any incident ray traveling towards a convex mirror where its extension passes through the focal point, will reflect and travel parallel to the principle axis.

A convex mirror is sometimes referred to as a diverging mirror. It is called that because the incident light originating from the same point will reflect off the mirror surface and diverge. When you look at the diagram, the reflections go out into all different directions.

Ray diagrams for convex mirrors: Convex mirror characteristics [|Concave mirror video] [|The convex mirror video]
 * 1) Pick a point on the top of an object and draw to incident rays going towards the mirror
 * 2) Reflect them
 * 3) Locate and mark the image of the top of the object
 * located behind the convex mirror
 * a virtual image
 * an upright image
 * reduced in size
 * Equation- the equation is the same as the concave equation

<span style="color: #6400ff; display: block; font-family: 'Comic Sans MS',cursive; font-size: 180%; text-align: center;">Lesson 35: __**Pulses**__ There are 2 pulses on the behavior of a pulse on a rope. First, there is a reflected pulse which is the disturbance that returns to the left after bouncing off the boundary. There is also the transmitted pulse which is the disturbance that continues moving to the right. __**Refraction**__

Refraction is the bending of the path of light. When refraction occurs, light passes from one medium into a second medium, but only occurs at a boundary. There is the wave front of light. Then there is a boundary between two media. The change in speed occurs for a wave of light. Finally, a light wave will not undergo refraction if it approaches the boundary in a direction that is perpendicular to it. It must go diagonal so that it is refracted, not at a perpendicular angle. __**Optical density**__ Optical density is the tendency of the atoms of a material to maintain the absorbed energy of an electromagnetic wave, showing the form of vibrating electrons before reemitting it as a new electromagnetic disturbance. The more optically dense, the slower the wave will move through the material.__**Index of refraction**__To show an indication of optical density, there is the index of refraction. The index of refraction is a numerical index value that expresses a value relative to the speed of light in a vacuum. The values show a measure of relative speed of a light wave in a particular medium. To find the index of refraction you do n(index of refraction= 3 x 10^8 / vmaterial. __**Short definitions**__ Light traveling fast to slow- goes towards the normalLight traveling slow to fast- ray will bend away from the normalLeast time principle- light always takes the path that requires the least amount of time

In this picture above, for any given angles of incidence, the angle of refraction is dependent upon the speeds of light in the two materials. The speed depends on the optical density and the index of refraction values of the two materials. the angles that the light rays make with the normal to the indices of refraction of the two materials on each side of the boundary have a mathematical relationship which is also known as Snell’s law. The equation: The way you need to draw the diagram:

[|refraction video] [|Refraction mathematics video] <span style="color: #ac00ff; display: block; font-family: 'Comic Sans MS',cursive; font-size: 180%; text-align: center;">lesson 36: __**Total internal reflection**__ Total internal reflection is the total amount of incident light at the boundary between two media. There are 2 rules for internal reflection. First, the light must be in the more dense medium and approach the less dense medium. Second, the angle of incidence is greater than the critical angle. But the angle of incidence must be large and the maximum angle of refraction is 90 degrees and the angle of incidence must be greater than 48.6 degrees to have TIR occur. __**Critical Angle**__ The critical angle is the angle of incidence value. But, when you look at the critical angle, the actual value of the angle depends on the combination of materials present on each side of the boundary. To calculate the critical angle, you must take the inverse sine of the ratio of the indices of refraction. (equation is critical angle= sin-1(nr/ni) index of refract) __**Angle of deviation**__ The angle of deviation is the angle made between the incident ray of light entering the 1st face of the prism and the refracted ray that emerges from the 2nd face of the prism. Because of the different indices of refraction, the angle of deviation varies with wavelength. __**Dispersion**__ Looking at ROYGBIV- The light refracts towards the normal when entering the glass and away from the normal upon exiting the glass. The violet wavelength refracts more than the red. When the light is exiting the prism, the light goes the opposite direction. There is no overall angle of deviation for the different colors of white light. There is a thin red fringe present on one end of the beam and thin violet fringe present on the opposite side of the beam. The fringe represents the dispersion. Then you can see the dispersion shows the spectrum of wavelengths present in visible light. __** R a i n b o w **__ A rainbow can be a complete circle. There is a circle because there is a collection of suspended droplets in the atmosphere that are capable of concentrating the dispersed light at angles of deviation of 40-42 degrees relative to the original path of light from the sun. The droplets form a circular arc and they disperse light and reflecting it back towards the observer. Each drop refracts and disperses to the entire visible light spectrum. Red is refracted at a steeper angle and blue at a less steep angle. __**Mirage**__ A mirage is an optical phenomenon that creates the illusion of water and outcomes the refraction of light through a non-uniform medium. You can see a mirage when it’s a sunny day and you are driving. It looks like there is a puddle far ahead and when you get there, you don’t see it. This is an illusion. When there is less optically dense air, light is traveling downward and speeds up. The change in speed causes a change of direction. The light ray bends away from the normal, the ray would bend parallel to the roadway and bends upward toward the cooler air. [|Total internal reflection video]

<span style="color: #ac00ff; display: block; font-family: 'Comic Sans MS',cursive; font-size: 180%; text-align: center;">lesson 37: __**Converging and diverging lens**__ A converging lens is a lens that converges rays of light that are traveling parallel to its principal axis. You can tell when a lens is converging because they are thick across the middle and thin at the upper and lower edges. A diverging lens is a lens that diverges rays of light that travel parallel to its principle axis. They are thin across the middle and thick at the upper and lower edges. __**Double convex and concave lenses**__ A double convex lens is symmetrical across both its horizontal and vertical axis. Because of the thicker middle, converge rays of light travel parallel to its principal axis. A double concave lens is symmetrical across its horizontal and vertical axis. Since the concave lens is thinner at the middle, it will diverge rays of light that travel parallel to its principal axis. __**Converging lenses and characteristics**__ There are 3 rules for a converging lens. First, any incident ray traveling parallel to the principal axis of a converging lens will refract through the lens and travel through the focal point on the opposite side of the lens. Second, any incident ray traveling through the focal point on the way to the lens, will refract through the lens and travel parallel to the principal axis. Last, an incident ray that passes through the center of the lens will continue in the same direction when it entered the lens.
 * the object is located //beyond//the 2F point
 * Inverted
 * Reduced
 * real
 * the object is located at the 2F point
 * equal in size
 * inverted
 * real
 * the object is located between the 2F point and the focal point
 * inverted
 * enlarged
 * real
 * the object is located at the focal point
 * NO IMAGE
 * the object is located in front of the focal point
 * Upright
 * Enlarged
 * Virtual

__**Convex lens rules and Image characteristics**__ There are 3 rules for a convex lens. First, any incident ray traveling parallel to the principal axis of a diverging lens will refract through the lens and travel in line with the focal point. Second, any incident ray traveling towards the focal point on the way to the lens will refract through the lens and travel parallel to the principal axis. Last, an incident ray that passes through the center of the lens will continue in the same direction that it had when it entered the lens.
 * located on the object' side of the lens
 * a virtual image
 * an upright image
 * reduced in size

__**The eye**__ The retina is a location that is always the same distance away from the cornea. The results of the height of the image, distance of image, and distance of object concern 2 main topics about the ability of the eye. First, the distance between the observer and the object will greatly influence the image size and quality. The closer you are to an image, the bigger you think it is. The farther away, the smaller image but finer details are lost. Second, the varying distance between the observer and the object pose some problems for the human eye. To see far away, you use the cornea lens which changes the focal length [|converging lens video] [|diverging lens video]