Optics: Reflection and Refraction

          The purpose of this lab is to see how light is affected by passing through substance interfaces such as air to acrylic. When a light ray is perpendicular (normal) to a substance interface, the light ray passes through unchanged. When the light ray hits an interface with an incident angle other that a right angle, the light ray will bend if it passes into the substance. In this lab, an acrylic half circle was used to relate incident angle with the refracted angle. A light source was directed to the center of the half disk and measurements were taken over a range of angles. Two sets of data were collected. The first set uses the flat side of the half disk for the incident angle. The second set uses the curved side for the incident angle. The interface of interest in both scenarios is the flat side of the half disk.

Trial 1 (Incident angle on flat side)

Incident Angle (degrees)	Refracted Angle (degrees)	Sin of Incident Angle	Sin of Refracted Angle
60	144	0.886	0.587
55	148	0.819	0.53
50	152	0.766	0.5
45	152	0.707	0.47
40	156	0.643	0.407
35	158	0.574	0.375
30	161	0.5	0.326
25	163	0.423	0.292
20	167	0.342	0.292
15	172	0.299	0.139

Trial 2 (Incident angle on curved side)

Incident Angle (degrees)	Refracted Angle (degrees)	Sin of Incident Angle	Sin of Refracted Angle
30	124	0.5	0.829
25	135	0.423	0.707
20	149	0.342	0.515
15	152	0.259	0.469
10	167	0.174	0.225
5	174	0.087	0.105
0	180	0	0
-5	190	-0.087	-0.174
-10	203	-0.174	-0.391
-15	211	-0.259	-0.515

          The data sets for each trial provided two graphs which totaled in four graphs all together. The first graph was incident angle vs. refracted angle. The second graph was sine of incident angle vs. sine of refracted angle. The follow is the sets of graphs for each trial.


Trial 1:


Incident Angle vs. Refracted Angle





















Sine of Incident Angle vs.  Sine of Refracted Angle





Trial 2:


Incident Angle vs. Refracted Angle



 Sine of Incident Angle vs.  Sine of Refracted Angle


          When looking at the RMS for each fit, the relationship between sine of incident angle vs.  sine of refracted angle are more reliable with a much lower RMS than incident angle vs. refracted angle. This leads to the idea that the sine graphs show a true linear relationship where as the angle graphs might appear linear and yet they should not be. The slope of the sine graph for trial 1 should be one over the index of refraction for acrylic. The slope of the sine graph for trial two should be close to the value of index of refraction for acrylic. The actual value of acrylic index of refraction is 1.49. 

Trial 1:
 Slope of sine graph = 0.648
 Inverse of acrylic index of refraction = 0.671

Trial 2:
 Slope of sine graph = 1.76
 Acrylic index of refraction = 1.49


          These values are relatively close when considering the experiment setup and the inaccuracy of measuring a "beam" of light. In the picture of the setup above it is easily seen that the beam of light has an inherent thickness that changes over a distance. This cam make measurements inaccurate. Furthermore, a paper protractor can be fairly inaccurate as well if the light does not reach the hash marks on the protractor.


          These graphs lead to the relationship of sine of incident angle is proportional to refracted angle. This is also know as Snell's Law:

where n is index of refraction on either side of the interface and theta is either incident or refracted angle. It is simple to see that if one of the indices in the experiment is 1 (index of air), then the sine graph relationship is truly linear which was depicted in the sine graphs.