Jason Fong
702847140
Lab Section 3
Exp Date: 2-27-00
Physics 4BL: Experiment 7
This experiment explored the behavior of light. A prism, lenses of various
shapes, and combinations of those lenses were used to perform the experiment. A ray
box was used as the light source and different shaped filters were used to create one,
three, or five light rays from the ray box. The light rays were shone over a sheet of paper
so that the paths of the rays could be marked. The ray box was first adjusted so that the
rays that came out were parallel to each other. This was checked by setting the filter to
show five rays, and making sure that the distance between the rays remained constant.
The prism and lenses were placed in the path of the light to alter the path of the rays.
Snell’s Law and Critical Angle
The incident, reflected, and transmitted angles at each interface was measured.
The incident and reflected angles were found to be equal, as was predicted. Snell’s Law
states that
n1 sin i  n2 sin t
n1 is the index of refraction of the first material, air, which is approximately 1. n2 is the
index of refraction of the second material, the plastic prism. θi is the incident angle, and
θt is the transmitted angle. The index of refraction can be found after the angles are
measured.
n1 sin  i  n2 sin  t
n2 


n1 sin  i 1 sin 23

 1.418
sin  t
sin 16
The index of refraction for the plastic is 1.418. This value can be checking by using
Snell’s Law at the second interface as the light leaves the plastic and enters the air.
n1 sin  i  n2 sin  t
1.418sin 16   1sin 23 
0.3909  0.3907
The values are very close, so the index of refraction of the plastic is confirmed by Snell’s
Law.
The critical angle is the angle of incident that creates a transmitted angle of 90
degrees, giving total internal reflection. The critical angle is found by the following
formula (evaluated at the second interface).
sin  c 
n1
n2
 n1 
 1 

  sin 1 
  44.85
 1.418 
 n2 
 c  sin 1
The critical angle is 44.85 degrees.
Color Aberration
The prism was placed so that the light entered the triangular tip. The prism was
rotated so that the emerging beam was just about on total internal reflection. The light
that came out was split into the spectrum of light. The light that emerged followed the
pattern of red, orange, yellow, green, blue, indigo, violet. The red end of the spectrum
was defracted the least, and the violet end of the spectrum was defracted the most. The
colors are seperated because the light is traveling through more of the prism at the angle
it is at, and because different colors are defracted different amounts, the colors separate
into the spectrum of visible light.
The refractive index of the reddest and the most violet light can be calculated.
The reddest light has a refractive index as follows:
n2 sin  i  n1 sin  t
n1 


n2 sin  i 1.418 sin 43

 0.982
sin  t
sin 80
The most violet light has a refractive index as follows:
n2 sin  i  n1 sin  t
n1 


n2 sin  i 1.418 sin 43

 0.968
sin  t
sin 88
Since the angles had an uncertainty of ±1 degree, the refractive indices have an
uncertainty of about ±0.005 Thus, the difference in refractive indices of the red and
violet light is 0.014 ± 0.005.
Lenses
The focal length of each lens is noted in the following table.
Bi-convex
5.75 cm
Bi-concave
-3.90 cm
Plano-convex
9.40 cm
(flat side to light source)
Plano-convex
10.30 cm
(round side to light source)
Spherical Aberration
When five light rays were shone three the bi-convex lens, three focal points were
observed. There was a focal point for the central three rays, the leftmost two rays, and
the rightmost three rays. The distance between the left and right focal points was 0.25
cm. The distance from the midpoint between those two focal points to the lens was 5.10
cm. The focal length of the left and right focal points was 5.10 cm. The focal length of
the central rays was 5.50 cm. The focal length of the left and right focal points is 7.27%
less than the focal length of the central rays.
One-Dimensional Magnification
When the parallel light rays pass through the bi-concave and plano-convex lenses,
they can be made to emerge as parallel rays if the lenses are arranged correctly. The
separation distance between the rays can be either magnified or reduced, depending on
the order of the lenses. When the light passed through the bi-concave lens first and then
through the round side of the plano-convex lens, the rays were magnified and changed by
a factor of 1.89. When the light passed through the flat side of the plano-convex lens
first, and then through the bi-concave lens, the rays were reduced and changed by a factor
of 0.47.
Lens Combination
The lensmaker’s equation states theat a combination of two lenses placed with
their axes parallel and in direct contact with one another are equivalent to a single lens
with a focal length given by the following formula.
1 1 1
 
f
f1 f 2
For this part of the experiment, the bi-concave and plano-convex lenses were put into
combination by placing them into contact with each other. The light rays passed through
the flat side of the plano-convex first, then through the bi-concave lens. Based on the
focal lengths measured for each lens alone, the lensmaker’s formula predicts that the
focal length will be:
1 1 1
 
f
f1 f 2
1
1
1 1
 1

1
  6.67 cm
f      

 9.4 cm  3.9 cm 
 f1 f 2 
Thus, the predicted focal length is –6.67 cm. The negative means that the light rays
diverge, which is what was observed. The actual focal length measured was –8.40 cm.
The measured focal length is 25.9% greater than the predicted focal length. The large
discrepancy could be caused by the surface between the lenses. The surfaces are not
perfectly smooth so the light may change path when moving between the two lenses.
Also, since the lenses may not have been an exactly perfect fit, the light may have
changed path when moving between a tiny air space between the lenses.