Introduction to Reflection and Refraction

Introduction: 

The nature of refraction and reflection angles may be explored with the aid of a semicircular acrylic glass piece.  In this experiment, we will explore the how light propagates through two different mediums. Namely, air and acrylic glass.  Air is approximated as vacuum with an index of refraction of 1.  Alerting our apparatus setup will allows to observe the critical angles of incidence.

Steps:

The apparatus requires the acrylic glass piece, a light box, a voltage generator, and a protractor.
Setup 1:
The light beam is aimed at the center of the flat side and exits through a radial path of the glass piece. Since we approximate air as vacuum it has the lower density of the two mediums.  The acrylic has the higher density.  Hence we go from low-high-low densities (once the lights exits back to air).

The setup for our first experimental run.  Angle of incidence is 0 degrees here.

Varying the angle of incidence by 5 degrees on each measurement we obtain the refraction angle along with their sin values.



θ1 θ2 sinθ1 sinθ2
0   0 0.000 0.000
5 3.5   0.087 0.061
10 5      0.174 0.087
15 9.3   0.259 0.162
20 12.6 0.342 0.218
25 16 0.423 0.276
30 17.5 0.500 0.301
35 22.2 0.574 0.378
40 25.5 0.643 0.431
45 28.5 0.707 0.477
50 31.5 0.766 0.522
55 35 0.819 0.574
60 37.5 0.866 0.609


Uncertainties (+/-)
uθ1 uθ2 usinθ1 usinθ2
1 1 0.017 0.017
1 1 0.017 0.017
1  1 0.017 0.017
1 1 0.017 0.017
1 1 0.016 0.017
1 1 0.016 0.017
1 1 0.015 0.017
1 1 0.014 0.016
1  1 0.013 0.016
1 1 0.012 0.015
1 1 0.011 0.015
1  1 0.010 0.014
1  1 0.009 0.014

We obtain the following graphs:

θ1 vs θ2

sinθ1 vs sinθ2

θ1 vs θ2 
mθ ≈ .64
sinθ1 vs sinθ2
msinθ ≈ .66

sinθ2/sinθ1 = .66

Setup 2:
The second setup involves using the curved surface of the semicircular acrylic.  Aiming the light beam at the curved surface and to the center of circle, we obtain straight beams passing through the piece.  This happens because the light beam is normal to the surface and thus creates a 0 degree angle of incidence.
The data obtained is shown below.

Curved surface incidence.

θ1 θ2 sinθ1 sinθ2
0 0 0.000 0.000
5 9.5 0.087 0.165
10 16.5 0.174 0.284
15 24.5 0.259 0.415
20 34 0.342 0.559
25 44 0.423 0.695
30 51.5 0.500 0.783
35 64.5 0.574 0.903
40 80    0.643 0.985


Uncertainties (+/-)
uθ1 uθ2 usinθ1 usinθ2
1 1 0.017 0.017
1 1 0.017 0.017
1         1 0.017 0.017
1 1 0.017 0.016
1 1 0.016 0.014
1 1 0.016 0.013
1         1 0.015 0.011
1 1 0.014 0.008
1         1 0.013 0.003


Similarly, we produce the following graphs:

θ1 vs θ2

sinθ1 vs sinθ2

θ1 vs θ2 
mθ ≈ 1.6 (ignoring 20 degree angle)
sinθ1 vs sinθ2
msinθ ≈ 1.5 


Questions/Conclusions:

We notice that beyond 40 degree we run into an issue when refraction no longer occurs and, instead, the light beam is completely reflected back inside the acrylic.

Using the axis variable we may fit have the equation:
sinθ2/sinθ1 = 1.5

This relationship is exactly inversely proportional to the equation obtained obtained in setup 1.  This is expected as the light beam, in setup 1, goes from low to high index of refraction mediums.  Setup 2 represents the opposite pathway.

The slope for setup 2 represents the refractive index.  The actual values for the refractive index of acrylic glass vary usually around a value of 1.49.