Unit3B_KoscielnyD

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toc = Lessons 32 & 33 =

Electromagnetic Waves
-can travel through a vacuum - source is accelerating, charged particles - electric and magnetic components travel at the same time - electromagnetic spectrum= entire spectrum of electromagnetic radiation we know- 10^4 Hz to 10^24 Hz from small to long wavelengths (high to low frequency) - all electromagnetic waves travel at c, the speed of light, 3E8, in a vacuum - linear propagation= it always travels in a straight line - energy due to frequency NOT amplitude as with mechanical waves

Light
- an electromagnetic wave - 10^14Hz V I B G Y O R - as you change **optical density** you change speed- the more dense, the slower the wave goes, the smaller the wavelength - **Opaque**= absorbs or reflects all, no transmission of energy - **Translucent=** partial transition, partial absorption - **Transparent**= light passes through- gets re-admitted: full transmission of energy - frequency always stays the same - light-year- how far (distance) light travels in a year - Different early theories/experiments of what light is: - every point on a wave is the source for the next wav- interferes

Diffraction of Light
- light bends around an obstacle or through an opening create an interference pattern (due to Huygen's principle) - for diffraction, wavelength must be on the same order of magnitude as the opening/obstacle so it has to bend - the bigger the opening the less diffraction - interference pattern of 2 slits looks similar to the diffraction pattern of1 slit - central anti-node is same width and same brightness as the fringe - as distance increases you get a closer pattern - diffractiong grating has hundreds or thousands of slit per mm - as wavelengths decrease, the pattern gets closer

Image Characteristics
Two types: Orientation: **upright** (right side up) or **inverted** (upside down) Size: **Large** (larger than original/ actual object), **Uncahanged**, or **Reduces** Location: relative to the optical plane and/or the focal point
 * Real**- formed when light is actually at the position it seems to be- it can be projected on to something
 * Virtual**- light is not really where it seems to be- brain's interpretation- reflection- cannot be projected

Plane Mirror Lab

 * Objectives: ** Demonstrate that reflection from a plane surce the angle of incidence is equal to the angle of reflection.


 * Materials: ** Optical Bench, Light source, circular reflecting surface, protractor, straight edge, compass, pencil, black tape, white and/or tracing paper.

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 measurded 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.
 * Theory **
 * Reflection **

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.


 * Procedure **
 * Part A: Reflection **


 * 1) 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) Set the mirror so that its back is on the line.
 * 3) Trace the angle of reflection lightly, by making a few dots.
 * 4) Repeat for each angle of incidence.
 * 5) 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.

Analysis
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.

Data Table 1: Reflection

 * **Ray ** || **Angle of Incidence, **** q ****1 ** || **Angle of Reflection, **** q ****2 ** || **Difference in Angles (degrees) ** || **Percent Error ** || **Percent Error with 1 degree adjustment ** ||
 * **1 ** || 15 || 16 || 1 || 6.67% || 0% ||
 * **2 ** || 30 || <span style="color: #000000; display: block; font-family: "Times New Roman",serif; font-size: 16px; text-align: right;">31 || <span style="color: #000000; display: block; font-family: "Times New Roman",serif; font-size: 16px; text-align: right;">1 || <span style="color: #000000; display: block; font-family: "Times New Roman",serif; font-size: 16px; text-align: right;">3.33% || <span style="color: #000000; display: block; font-family: "Times New Roman",serif; font-size: 16px; text-align: right;">0% ||
 * **<span style="color: #000000; font-family: "Times New Roman","serif"; font-size: 16px;">3 ** || <span style="color: #000000; display: block; font-family: "Times New Roman",serif; font-size: 16px; text-align: right;">43 || <span style="color: #000000; display: block; font-family: "Times New Roman",serif; font-size: 16px; text-align: right;">42 || <span style="color: #000000; display: block; font-family: "Times New Roman",serif; font-size: 16px; text-align: right;">1 || <span style="color: #000000; display: block; font-family: "Times New Roman",serif; font-size: 16px; text-align: right;">2.33% || <span style="color: #000000; display: block; font-family: "Times New Roman",serif; font-size: 16px; text-align: right;">0% ||
 * **<span style="color: #000000; font-family: "Times New Roman","serif"; font-size: 16px;">4 ** || <span style="color: #000000; display: block; font-family: "Times New Roman",serif; font-size: 16px; text-align: right;">57 || <span style="color: #000000; display: block; font-family: "Times New Roman",serif; font-size: 16px; text-align: right;">56 || <span style="color: #000000; display: block; font-family: "Times New Roman",serif; font-size: 16px; text-align: right;">1 || <span style="color: #000000; display: block; font-family: "Times New Roman",serif; font-size: 16px; text-align: right;">1.75% || <span style="color: #000000; display: block; font-family: "Times New Roman",serif; font-size: 16px; text-align: right;">0% ||
 * **<span style="color: #000000; font-family: "Times New Roman","serif"; font-size: 16px;">5 ** || <span style="color: #000000; display: block; font-family: "Times New Roman",serif; font-size: 16px; text-align: right;">66 || <span style="color: #000000; display: block; font-family: "Times New Roman",serif; font-size: 16px; text-align: right;">65 || <span style="color: #000000; display: block; font-family: "Times New Roman",serif; font-size: 16px; text-align: right;">1 || <span style="color: #000000; display: block; font-family: "Times New Roman",serif; font-size: 16px; text-align: right;">1.52% || <span style="color: #000000; display: block; font-family: "Times New Roman",serif; font-size: 16px; text-align: right;">0% ||



Analysis Questions
Yes- there is simply 1 degree error for each, probably due to tracing error. I think I may have measured on either side of the beam of light, not through the center. The error seems to go down but that is simply because the angle is going up- the actual difference in degrees stays constant. To demonstrate this I made another column in my data table with a 1 degree adjustment.
 * 1) Are your data consistent with the law of reflection? State your answer as quantitatively as possible.

Behind the mirror.
 * 1) Where is the image in a plane mirror located?

The graph would be directly proportional and the slope would be 1 (were the data completely accurate) because the angles of incidence and refraction are equal.
 * 1) If you were required to graph the angle of incidence vs. the angle of reflection, what would be the shape of the graph? What would the slope of the line be?

They are located behind the mirror, upright, at the same size as the object, and virtual. = = = = = = = Homework  = **Reading Summary:**
 * 1) What are the characteristics of all images from plane mirrors?

__Wave-like Behaviors of Light__ As a wave, light exhibits interference patterns, the doppler effect, reflection, refraction, and diffraction.

__Two Point Source Interference__ Light waves undergo interference similarly to sound waves, **coherent light** occurs when two light sources are admitting light **in phase** (admitting nodes and anti-nodes at the same exact times).

__Thin Film Interference__
 * Thin film** **interference** is apparent in thin films of water or oil that show a spectrum of colors due to interference.

__Polarization__
 * Unpolarized light** travels on more than one plane, so you can eliminate parts of it by **polarizing** it, making it less intense.

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__Anatomy of a Two-Source Interference Pattern__ The **central anti-nodal line** extends out from the source, the first, second, third, and so-on **anti-nodal lines** are those 1,2,3 and so anti-nodes to either side of the central one; there are **nodal lines** (first, second, third, and so on) between the anti-nodal lines; each line has an order number (m=?).



__The Path Difference__ __Young's Equation__ Interference forms a pattern of **maxima** (maximum intensity) and **minima** (minimum intensity), young's equation is: ** = y • d / (m • L).**
 * Path of difference** or **PD** is the difference between how far each wave has to travel to reach a certain point, found using this equation:**PD = | S1A - S2A | = | (source1)[[image:http://www.physicsclassroom.com/Class/light/lambda.gif width="7" height="8" align="bottom"]] - (source 2)[[image:http://www.physicsclassroom.com/Class/light/lambda.gif width="7" height="8" align="bottom"]] | = 1 [[image:http://www.physicsclassroom.com/Class/light/lambda.gif width="7" height="8" align="bottom"]]**

__Young's Experiment__ Young split a beam of sunlight into 2 coherent beams.

__Other Applications of Two Point Source Interference__ Most non-light applications involve radio-waves.

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__The Role of Light to Sight__ Without light, there would be no sight; to see we need **luminous objects** (things that emit light) to illuminate **illuminated object**.

__The Line of Sight__ To be able to see something, you **line of** **sight** must include that object, and to see an object in a mirror you must be able to see the image, which will be at the same distance from the mirror as the object.

__The Law of Reflection__
 * The law of reflection** tells us that the **angle of reflection** will equal the **angle of incidence** from the **normal line** (**N**) so the **reflected ray** will mirror the **incidence ray** across N.

__Specular vs. Diffuse Reflection__ Reflection off a shiny surface is **spectral** while reflection off a rough surface is **diffuse**.

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__Why is an Image Formed?__ The image is formed the same distance from the mirror as the object is on the other site but can only be seen by an observer if the observers **line of sight** intersects with the mirror on the way to the object.

__Image Characteristics for Plane Mirrors__ Mirrors form a **virtual image** as opposed to a **real image** because the **image location** is not actually where the light is located, in a plane mirror, the image is **upright** as opposed to **inverted** and there is a **right-left reversal**.

__Ray Diagrams for Plane Mirrors__ A **ray diagram** shows lines of sight and image location based the path light takes.

__What Portion of a Mirror is Required to View and Image?__ You only need a mirror half you height to see your full body.

__Right Angle Mirrors__ There are three images formed in a right angle mirror; 2 **primary images** and one **secondary image** in the corner- the secondary image doe not have right-left reversal.

__Other Multiple Mirror Systems__ The smaller there angle of two mirrors is, the more reflections of reflections, the more images.

**Cartoons:**

image: http://1.bp.blogspot.com/-e5V5kNhf8Lg/TeTEdFrlaMI/AAAAAAAAATM/ouGLELYAzmw/s1600/electromagnetic_spectrum_big.jpg website: http://theartinscience.blogspot.com/2011/05/infinitely-useful-em-diagram.html

image: http://imgs.xkcd.com/comics/seismic_waves.png website: [] = Lessons 34 & 35 =

Image Characteristics
- "LOST" "Two Old Super Lions" - Specular refflection- surface is flat - diffuse reflection- surface is irregular
 * - Location**
 * - Orientation**
 * - Size**
 * - Type**

Images Produced in Mirrors
if length is negative focal length- DIVERGING readius= radius of the sphere the mirror was cut from

Curved Mirror Lab
__Class Activity: *** are these the labs you want?__

(cm) ||
 * Object Distance (cm) || Focal Length (cm) || Calculated Image Distance (cm) || Experimental Image Distance
 * 48 || 5 || 5.5 || 5.4 ||
 * 18 || 5 || 6.9 || 6.6 ||
 * 23 || 10 || 17.7 || 17.3 ||
 * 48 || 10 || 12.6 || 12.6 ||

__Individual Activity:__ Analysis: - the focal length for both are the same, at around 2.3 cm. - the extensions of the lines did not form perfect points, but though they are not precise they are accurate. - we already know that the convex was virtual while concave was real

Reffraction Lab
- when a wave passes to another medium, it changes the speed, causing the wave to bend - light takes the path of least resistance that will allow it to travel the fastest





=Calculations=
 * Make a graph of sin θi vs sin θr.
 * (above)**
 * Use your graph of sin θi vs sin θr to find the equation of the line. Record this equation and the correlation coefficient.
 * n*sin θi = n(air)*sin θr**
 * sin θi****= n(air)*sin θr****/n**
 * sin θi****=1*sin****θr****/1.4855**
 * Y=x/1.4855**
 * 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//.)
 * n*sin θi = n(air)*sin θr**
 * n=1*****sin θr*****sin θi**
 * n=****sin θr*****sin θi**

=Analysis Questions=
 * 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!)
 * %error= |(theo-exp)/theo| **
 * %error= |(1.5-1.4855)/1.5| **
 * error= 0.98% **

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)?
 * 1) Choose one: always smaller, __**always bigger**__, or always constant.
 * 2) Provide evidence from the lab.
 * The angle of refraction was smaller than the angle of incidence for all angle in this lab from the smallest through the greatest.**

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?
 * 1) Choose one: __**always smaller**__, always bigger, or always constant.
 * 2) Provide evidence from the lab.
 * The evidence from #1 still applies because mathematically the angle works backwards as well.**
 * 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.**__

4) Discuss how the angle of refraction changed with the angle of incidence. As the angle of incidence increased, the angle of refraction
 * 1) __**Increased.**__
 * 2) Decreased.
 * 3) Remained the same.

= Homework  = **Reading Summary:** __The Anatomy of a Curved Mirror__ The diameter of a curved mirror is the **principal axis**, which meets the mirror at its **vertex**, the radius is the **radius of curvature** is between the vertex and the **center of curvature** (**C**), and the **focal point** is half of the radius.

__Reflection of Light and Image Formation__ Concave mirrors can produce real images.

__Two Rules of Reflection and Image Formation__ A ray traveling parallel to the p-axis will reflect through the focal point and a ray traveling through the focal point will reflect parallel.



__Ray Diagrams- Concave Mirrors__ use the rules to find the Image location.

__Image Characteristics for Concave Mirrors__ The general LOST will be same for certain ranges of the diagram. 1: 2: 3: 4: 5: __The Mirror Equation- Concave Mirrors__ You use the **mirror equation** to find object distance (do), image distance (di), and focal length (f) and the **magnification equation** finds the ratio of the image height (hi) and object height (ho) distance ratio. __Spherical Aberration__ At the edges of the mirror the light undergoes **abberation** and does not go through the focal point; thus, the image can be made more clear if you cover the edges. ---

__Reflection of Light and Image Formation for Convex Mirrors__ A ray traveling parallel to the principal axis will reflect so the extension will pass through f and a ray traveling so its extension will pass through f will go parallel at the mirror. __Ray Diagrams- Convex Mirrors__ Use the rules to find the image. __Image Characteristics for Convex Mirrors__ All images will be located behind the mirror, upright, reduced size, and virtual. __The Mirror Equation- Convex Mirrors__ Use the equations the same way you did for concave.

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__Boundary Behavior__ When any kind of wave hits a boundary (at a non-right angle for light),part is **transmitted** and **refracted** and part is **reflected**.

__Refraction and Sight__  Refraction of light causes things to look out of place when they are viewed through a transparent material.



__The Cause of Refraction__ Light bends (changes angles) when it hits a boundary.

__Optical Density and Light Speed__ Speed and change in speed depends on **Optical Density** also called **the index of refraction**.

__The Direction of Bending__ The **normal line** is a line perpendicular to the boundary, the angles are measured from this line.

__If I were an Archer Fish__ Archer fishes know how to shoot prey above the water despite refraction.

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__The Angle of Refraction__ The **angle of refraction** depends on **optical density**.

__Snell's Law__ Snell's law is

__Ray Tracing and Problem-Solving__
 * Layer problems** are when you must calculate for more than one boundary.

__Determination of n Values__ The **index of refraction** (n) can be found experimentally by finding the point at which all light is reflected rather than transferred.

**Cartoons & Cool Picture:**



image: [] website: [] Image: http://icanhascheezburger.wordpress.com/files/2007/12/funny-pictures-mirror-cat.jpg Website: []

Image: [] Website: [] = = = = = = = = = Lessons 36 & 37 =
 * work is on paper
 * remember to use an arrow in the diagrams

Lenses Lab

 * NO ANALYSIS Qs**
 * Data:**
 * Calculations:**

= Homework  = **Reading Summary:** __Boundary Behavior Revisited__ Review

__Total Internal Reflection__ __The Critical Angle__ The **critical angle** is the angle of incidence at which there is TIR- no light escapes, it is all reflected back into the prism/other material; it can be found mathematically by using 90 degrees for the angle of refraction.
 * Total internal reflection** (as described by the bellow image) allows **optical fibers** to transmitting light.

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__Dispersion of Light by a Prism__
 * Dispersion** is the dividing of white light into all colors (**ROYGBIV**) at the **angle of deviation**.

__Rainbow Formation__ Rainbows are formed when sunlight behind a storm refracts, sending light to the observer in the ROYGBIV.*
 * __Mirages__**
 * A** Mirage **an optical illusion of water due to refraction through a non-uniform*** medium, usually during hot days.

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__The Anatomy of a Lens__ A **lens** is a transparent material made to take advantage of refraction... ...it can be **Convex/Double Convex** (converging) or **Concave/Double Concave** (diverging)...

... and has an anatomy similar to that of a mirror based around its **vertical axis**. __Refraction by Lenses__ The rules of refraction for different lenses (as seen bellow) are similar to the rules for mirrors, but there is annother rule aplng to both types of lenses saying that an i ray traveling through the exact center of the lens will continue on its path.



__Image Formation Revisited__ Lenses change the apparent image location. __Converging Lenses: Ray Diagrams__ Use rules to find image location and height with to-scale diagrams. __Converging Lenses: Object-Image Relations__ Even without the diagram you can tell where the image will be if you know where the object is in respect to the lens. 1: 2: 3: 4: 5: __Diverging Lenses: Ray Diagrams__ Use rules to find image location and height with to-scale diagrams. __Diverging Lenses: Object-Image Relations__ The placement in diverging lenses is always between f and the lens, and the height depends on how far away the object is. __The Mathematics of Lenses__ As with mirrors, you use the **lens equation** and the **magnification equation** to find focal length as well as object and image location and height.

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__The Anatomy of the Eye__ The **pupil** is a hole through which light passes to the rest of the eye's anatomy (bellow). __Image Formation and Detaction__ The prosess illustracted bellow is known as **accommodation**.

__The Wonder of Accommodation__ The **ciliary muscles** like the focus on a camera lens in accommodation to bring light to the **fovea centralis**. __Farsightedness and its Correction__ Converging lenses can be used to compensate for **hyperopia** (**farsightedness**).

__Nearsightedness and its Correction__ Diverging lenses can be used to compensate for **myopia** (**nearsightedness**).

**Cartoon:** image: http://www.cartoonstock.com/newscartoons/cartoonists/jdi/lowres/jdin695l.jpg website: []