The purpose of this experiment was to test the validity of the Law of Reflection and Snell's Law (Also known as the Law of Refraction).
Reflection is defined as the reversal in direction of a particle stream or wave upon encountering a boundary. The law of reflection states that the angle of reflection and angle of incidence are equal, with each angle being measured from the normal to the boundary:
Refraction is defined as the bending of light that takes place at a boundary between two materials having different indices of refraction due to a change in the speed of light as it passes from one medium to another. The Law of Reflection (Snell's Law) states that the ratio of the sines of the angles of incidence and refraction is equivalent to the ratio of velocities in the two media, or equivalent to the opposite ratio of the indices of refraction: During the course of analyzing our data, we calculated the index of refraction for the plastic lens and thereby the speed of light in the plastic.
The expected results that would need to occur to prove the validity of the Law of Reflection would be that when we conduct the experiment, the measure of the angle of incidence would have to be equal to the measurement of the angle of reflection, because this is what the Law of Reflection states.
The expected results that would need to occur to prove the validity of Snell's Law would be that as light passes the border between media, depending upon the relative refractive indices of the two media, the light will either be refracted to a lesser angle, or a greater one.
PROCEDURE:
The materials that were needed for this experiment were: a table, a pencil, paper for notes, a laser, a platform, and a lens. The setup of the materials was as shown:
Initially, before we began our experiment, we used the adjustment screws on the back of the laser to make sure that the laser-line went straight down the "normal" line on the platform.
PART ONE:
We aligned the flat side of the cylindrical lens along the line on the platform labeled "component." We were able to just barely see the edge of the "component line" under the edge of the lens. When it was precisely aligned, we saw that the laser followed the normal line all the way through the lens and across the platform, passing through the "zero" angle on both sides. We spent a minute adjusting the lens until we were satisfied and had it in the right position. The lens slipped at times during the experiment, and we recentered it on the "zero" angle.
Without moving the lens, we rotated the platform in both directions and observed the incident ray, the faint ray that was reflected from the flat surface, and the more intense refracted ray that exited the curved surface. We noticed now that all three rays fell along a measured angle from the normal line.
On a separate sheet of paper, we created Table 1 with seven columns and ten rows to document the data we observed while we conducted our experiment.
Not moving the lens, we rotated the platform so the incident ray came in at 10.0° on one side of the normal and read the angles of the reflected ray and the refracted ray and recorded these angles (to the closest half degree) under the appropriate columns on our table.
Not moving the lens, we rotated the platform 10.0° on the other side of the normal and recorded the angles of reflection and refraction
We repeated steps 5 and 6 for the rest of the angles of incidence and checked frequently to make sure that we had not disturbed the lens.
PART TWO:
We rotated the platform all the way around, without disturbing the lens of course, until the ray was incident on the curved side of the lens. The flat side of the lens was still lined up with the "component" line on the platform, and the laser was aligned with the "normal" line all the way across the platform.
We observed what happened to the ray as it emergeed from the flat side of the lens and went into the air.
We created Table 2 with six columns and ten rows to document the data observed.
After taking our measurements, we rotated the platform so the incident ray moved from "normal" to 90° and back. We observed the reflected ray inside the lens just as the refracted ray disappeared and made a note of our observation.
DATA:
REFLECTION AND REFRACTION (PART ONE)
ANGLE OF INCIDENCE (ΘI)
+ ANGLE OF REFLECTION
(ΘR+)
- ANGLE OF REFLECTION (ΘR-)
AVERAGE (ΘR)
+ ANGLE OF REFRACTION (Θ2+)
- ANGLE OF REFRACTION (Θ2-)
AVERAGE (Θ2)
10.0°
10.0°
10.0°
10.0°
7.0°
7.0°
7.0°
20.0°
13.0°
13.0°
13.0°
13.0°
13.0°
13.0°
30.0°
31.0°
29.0°
30.0°
20.0°
21.0°
20.5°
40.0°
41.0°
39.0°
40.0°
26.5°
25.0°
25.8°
50.0°
51.0°
49.0°
50.0°
31.5°
30.5°
31.0°
60.0°
61.0°
59.0°
60.0°
36.0°
35.5°
35.8°
70.0°
71.0°
68.0°
69.5°
39.5°
41.0°
40.3°
80.0°
81.5°
79.0°
80.3°
42.0°
42.0°
42.0°
85.0°
86.0°
83.0°
84.5°
42.5°
42.0°
42.3°
88.0°
89.0°
87.0°
88.0°
43.0°
43.0°
43.0°
QUALITATIVE OBSERVATIONS: We observed that not every material was aligned perfectly straight, that the lens got moved accidentally which would lead to error, that the laser got moved accidentally which would lead to error, and that the reflection data increased at a greater rate than the refraction rate.
REFLECTION AND REFRACTION (PART TWO)
ANGLE OF INCIDENCE (ΘI)
SINE (ΘI)
+ ANGLE OF REFRACTION (Θ2+)
- ANGLE OF REFRACTION (Θ2-)
AVERAGE (Θ2)
SINE (Θ2)
10.0°
0.174
15.0°
15.5°
15.3°
0.264
20.0°
0.342
30.0°
31.0°
30.5°
0.508
30.0°
0.500
47.0°
46.0°
46.5°
0.725
32.0°
0.530
51.0°
51.0°
51.0°
0.777
34.0°
0.559
56.0°
56.5°
56.3°
0.832
36.0°
0.588
61.0°
61.5°
61.3°
0.877
38.0°
0.616
66.0°
66.5°
66.3°
0.916
40.0°
0.643
72.0°
73.0°
72.5°
0.954
41.0°
(Last angle of visible refraction)
0.656
77.0°
77.0°
77.0°
0.974
QUALITATIVE OBSERVATIONS: We observed that the laser got moved accidentally which may have induced an error, and the angle of refraction disappeared at approximately 41°.
CONCLUSION:
In conclusion, the purpose of this experiment, to test the validity of the Law of Reflection and Snell's Law (Also known as the Law of Refraction), was fulfilled after the completion of the experiment because all of the data pointed to favor the two laws.
The Law of Reflection is supported in Graph 1 because the law states that the angle of incidence is equal to the angle of reflection, and in the plotted graph, for every y-value, the x-value was nearly the same, and the slope of the linear graph was one, meaning that the graph was of the function y = x, which is the same format as the formula of the law of reflection ().
The Law of Refraction (Snell's Law) states that the index of refraction of a substance multiplied by the sine of the angle of incidence is equal to the index of refraction of some other substance multiplied by the sine of the angle of refraction. Snell's Law is supported in graph two because the points on the graph formed a parabolic curve with an apparent asymptote, or critical angle, at around 41°, wherein the ray of refraction stopped appearing if the angle of incidence was made any steeper. The occurrence fulfilled our expected result that as light passed the border between media, depending upon the relative refractive indices of the two media, the light will either be refracted to a lesser angle, or a greater one.
We noted that when the refracted ray began to disappear, the reflected ray began to become brighter. We believed that this was because the energy from the refracted ray was transferred to the reflected ray.
In part one and part two, we believed that there was no refraction as the ray left the curved side of the lens because it entered and left through the flat side, which made the photons not get disrupted or curved.
During our experiment, the angles of incidence were measured on both sides of the normal line because it gave the angles of reflection and refraction a more precise measurement. There were some differences between the '+' and '-' readings. Some things that might account for these differences would be human error in reading the degree measurement, or failure to properly align the lens straightly on the compound line.
The slope of the line in graph 2 represents the index of refraction or 'n' in the Snell's Law (The Law of Refraction), because y/x is equal to Sin (θi)/ Sin (θ2), which is, solving Snell's Law for either 'n,' you will get n1/n2 = Sin (θi)/ Sin (θ2), and n is the density of the medium through which the light passes or how easily light can pass though it. (1.00 = Index of Refraction in a Vacuum)
SOURCES:
http://www.sasked.gov.sk.ca/docs/physics/u3c12phy.html
http://scienceworld.wolfram.com/physics/Reflection.html
http://en.wikipedia.org/wiki/Snell's_law
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