Experiment 7: Introduction to Reflection and Refraction

Purpose: To find a relationship between the angle of incidence and the angle of refraction using a light source.

Materials:

• light box
• semicircular plastic prism
• protractor

Set Up:

 

A cover is placed over the light source to allow only a tiny slit of light to pass through. A plastic prism is laid on top of a protractor. When the prism is rotated the light entering the prism changes the angle it leaves the prism (otherwise known as the angle of refraction). The protractor is used to measure how much the angle changes once it passes through the prism. The angle that the light first hits the prism is known as the angle of incidence. We can find a relationship between the two angles by measuring angle changes in 5 degree increments and graphing the data. The first data table is when the angle of incidence hits the flattened side of the prism and leaves the curved side as shown in the picture above.

Prior to taking data some questions were asked about how the light would behave:

Case 1
light hitting the acrylic straight edge first
incidence angle(θ1)	refraction angle(θ2)	sin (θ1)	sin(θ2)
10	7	0.174	0.122
15	12	0.259	0.208
20	14	0.342	0.242
30	20	0.500	0.342
35	23	0.574	0.391
40	25	0.643	0.423
45	30	0.707	0.500
50	32	0.766	0.530
60	36	0.866	0.588
70	41	0.940	0.656

For this graph a linear fit will sufficiently define the slope of this data.


The slope of this line is the relationship between the two angles. It is called the index of refraction (n). For air the index of refraction is 1 and all values for n are greater than or equal to 1. The slope equation for this line is y = 1.4477x so the index of refraction for this graph is 1.4477.

For part 2 the orientation of the prism was changed:

Case 2 is the data we took for the light hitting the curved side of the prism first and leaving through the straight edge.

light hitting the acrylic with the circular edge first
incidence angle(θ1)	refraction angle(θ2)	sin (θ1)	sin(θ2)
0	0	0	0
5	7	0.087156	0.121869
10	15	0.173648	0.258819
15	24	0.258819	0.406737
20	35	0.34202	0.573576
30	53	0.5	0.798636
40	75	0.642788	0.965926
44	90	0.694658	1

10. Were you able to complete all 10 trials? What happened?

After we reached an angle of incidence of 44 degrees the angle of refraction disappeared.

11. Plot a graph of sin θ₁ vs. sin θ₂ for all the angles you recorded. Determine the regression line and find the slope. What do you think the slope represents? 





12. Using the axis variables, write the equation of this straight line.
 The equation of this line is y = 1.5151x so the index of refraction is 1.5151.

Summary:
The indexes are different but fairly similar in value. This value should be the index of refraction for acrylic. Although there is a measure of uncertainty in the angle values, the data still generated accurate results.