Experiment 7: Introduction to Reflection and Refraction

PURPOSE: The purpose of this experiment is to verify the properties that are related to reflection and refraction using two mediums to reflect and refract a beam of light.

FORMULAS AND DERIVATIONS:                        

PROCEDURE:

Setup of the light beam with protractor underneath semicircle glass medium.

Measurements of different angles at different angles of light beams.  

Reversing the semicircle and recording the refraction angles again.

DATA & ANALYSIS:


Before the experiment, there were some predicted results and phenomena that were expected. The angle of incidence for the light ray at the flat surface would be zero and the angle of refraction at the flat surface would also be zero as well. As the light ray leaves the plastic piece at the curved edge and goes into the air the light will travel straight out since the light ray travels straight as it comes in. In the first situation light travels from a lower density to a higher density. These predictions were verified after turning on the light observing the results.

Trial 1
θi	Error	θr	Error	Rad(θ1)	Error	Rad(θ2)	Error	sin(θi)	Error	sin(θr)	Error
10	± 1	7	± 1	0.1745	± 0.017	0.1222	± 0.017	0.1736	±0.841	0.1219	±0.841
15	± 1	10	± 1	0.2618	± 0.017	0.1745	± 0.017	0.2588	±0.841	0.1736	±0.841
20	± 1	12	± 1	0.3491	± 0.017	0.2094	± 0.017	0.3420	±0.841	0.2079	±0.841
30	± 1	21	± 1	0.5236	± 0.017	0.3665	± 0.017	0.5000	±0.841	0.3584	±0.841
40	± 1	24	± 1	0.6981	± 0.017	0.4189	± 0.017	0.6428	±0.841	0.4067	±0.841
45	± 1	32	± 1	0.7854	± 0.017	0.5585	± 0.017	0.7071	±0.841	0.5299	±0.841
50	± 1	28.5	± 1	0.8727	± 0.017	0.4974	± 0.017	0.7660	±0.841	0.4772	±0.841
60	± 1	35	± 1	1.0472	± 0.017	0.6109	± 0.017	0.8660	±0.841	0.5736	±0.841
70	± 1	39	± 1	1.2217	± 0.017	0.6807	± 0.017	0.9397	±0.841	0.6293	±0.841
80	± 1	40	± 1	1.3963	± 0.017	0.6981	± 0.017	0.9848	±0.841	0.6428	±0.841

For the 2nd Trial there were also predicted results that were stated. As the light ray hits the first curved surface of the semicircle prism, the light ray goes through as a straight light. This would occur because both the angle of incident and angle of refraction is zero. When the light ray comes out the flat surface there will be a refraction as it goes into the air. The experiment will has a situation where light travels from a higher density to lower density.

TRIAL 2
θi	Error	θr	Error	Rad(θ1)	Error	Rad(θ2)	Error	sin(θi)	Error	sin(θr)	Error
6	± 1	10	± 1	0.0960	± 0.0174	0.1745	± 0.0174	0.0958	±0.8414	0.1736	±0.8414
11	± 1	15	± 1	0.1920	± 0.0174	0.2618	± 0.0174	0.1908	±0.8414	0.2588	±0.8414
12	± 1	20	± 1	0.2094	± 0.0174	0.3491	± 0.0174	0.2079	±0.8414	0.3420	±0.8414
19	± 1	30	± 1	0.3316	± 0.0174	0.5236	± 0.0174	0.3256	±0.8414	0.5000	±0.8414
23	± 1	40	± 1	0.3927	± 0.0174	0.6981	± 0.0174	0.3827	±0.8414	0.6428	±0.8414
26	± 1	45	± 1	0.4538	± 0.0174	0.7854	± 0.0174	0.4384	±0.8414	0.7071	±0.8414
29	± 1	50	± 1	0.5061	± 0.0174	0.8727	± 0.0174	0.4848	±0.8414	0.7660	±0.8414
32	± 1	60	± 1	0.5585	± 0.0174	1.0472	± 0.0174	0.5299	±0.8414	0.8660	±0.8414
34	± 1	70	± 1	0.5934	± 0.0174	1.2217	± 0.0174	0.5592	±0.8414	0.9397	±0.8414
38	± 1	80	± 1	0.6632	± 0.0174	1.3963	± 0.0174	0.6157	±0.8414	0.9848	±0.8414

Slope of the line gives the ratio of the index of refraction of the two mediums

The inverse of the glass and air gives the inverse of the slope, thus an inverse ratio of the index of refraction between the two mediums.

Maximum Angle

42˚

There was also a trial to see at what point the angle of refraction becomes 90 degrees or in others others, not being able to see the light beam itself. This is also known as the critical angle and can only be obtained when there light traveling from an object with a higher index of refraction to an object with a lower index of refraction. The maximum value for the angle of refraction was recorded to being 42˚± 1. Using the law of refraction again and setting the second angle to 90 degrees gives us the equation θ_critcal=sin^-1(N_b/N_a). This equation can be used to verify the maximum angle value that was found in the experiment.

         

Theoretical Calculations:

Using the theoretical of refraction of 1.5 for glass, the experimental value of the maximum angle could be verified. The theoretical value of the critical angle was about 42 degrees which gives an exact value of the value from the theoretical. 

CONCLUSION

Using the law of refraction, N₁Sin(θ₁)=N₂Sin(θ₂), and setting θ₁ as the incident ray and θ₂ as the angle of refraction, we can set the equation as Sin(θ₁)/ Sin(θ₂)= N₂/N₁. The slope of the line can also be written as Sin(θ₂)/Sin(θ₁). Using the data of the first trial we can see that the slope is 0.6588, which is also equal to N₁/N₂. By setting the index of refraction of air to being 1, we can clearly see that N₂ = 1.52, and that it represents the index of refraction of glass. While N₁ represents the index of refraction of air with an integer value of 1. Similar results occur for trial two when the semicircle is reversed and the N­₁ is now the index of refraction of glass and N­₂ represents for the air. The slope of the given line in trial 2 gave a value of 1.6458. The percent difference between the two index of refraction for glass is about 7%. It can be verified that the two slopes of these graphs are inverses of ratio to each other. The critical angle formula was also verified by finding the maximum angle at which the light beam can refract in a situation where there is a higher index of refraction to a lower one. This can be verified because the ratio can never be greater 1 for an inverse sin value. The angle of refraction at or past the critical angle becomes 90 degrees and so it cannot be measured because  it cannot be seen. The relationship between the reflection and refraction as well as the critical angle was all verified using two mediums, glass and air. 

Maximum Angle

42˚