Snell’s Law: Determination of the index of refraction of a glass plate.
Purpose:
To use Snell’s law to determine the index of refraction of a glass plate.
Theory:
According to Snell’s law, the ratio of the indeces of refraction of the two media is equal to
the sines of their angles relative to the normal.
n1 sin  2

n2 sin 1
or
the ratio of
n1 sin 1  n2 sin  2
For this experiment, the two media are glass and air. The accepted value of the index of refraction for air is
1.00029 at 0°C (Edwards, 2003). The experimental value should not vary from this significantly. The type of glass
is unknown, but the index of refraction should be around 1.56 ± 0.09 based on the values of possible substances
as shown in Table 1 below.
Table 1.
Index of refraction of various glass-like substances at 20°C (Edwards, 2003).
substance
quartz glass (fused)
Plexiglass
glass (crown)
glass (crystal)
glass (flint)
index of refraction
1.46
1.51
1.52
1.54
1.65
A sample situation can be used to predict the relationship between the angles in air and glass. The indices of
refraction for air (nair = 1.0003) and glass (nglass=1.56) as well as a hypothetical angle of 25° in glass relative to the
normal to the surface should produce an angle of 41° in air, according to the following calculations:
nair sin  air  nglass sin  glass
sin  air 
nglass
nair
sin  glass
 1.56

sin 25   41
 1.0003

 air  sin 1 
This shows that because the index of refraction of glass is significantly greater than that of air, the angle in the
glass should be significantly less than that in air. The diagram for the experiment should be similar to the one
below (Figure 1) for the hypothetical situation given above.
Figure 1.
Predicted diagram for the glass and air if the angle in glass is 25° resulting in a 41° angle in air.
θglass = 25°
θair = 41°
Variables
dependent variable
(measured)
independent variable
(manipulated)
constants variables
Materials
square glass plate
cardboard

angle in air (θair)

angle in glass, resulting from different points chosen on the edge of the glass on
the opposite side of the stationary pin
the stationary pin remained in the same position throughout
the glass plate remained in the same position (<1mm motion)
the edges of the glass were assumed to be straight and uniform
the bottoms of the pins were sighted at the same level (horizontal)
all angles were measured relative to normals constructed at each trial point on
the edge of the glass





pins (2)
ruler
paper (8 ½”  11”)
protractor
Procedure Set up
 The sheet of paper was placed on the cardboard.
 The square glass plate was placed near one corner of the paper and the edge of the glass was traced to help
detect if the plate moved during the experiment and to help re-establish its original position
 One pin was stuck into the paper/cardboard on the edge of the glass nearest the 8½” edge of the paper.
This is the stationary pin that remained in the same position throughout the experiment
 Four points on the opposite side of the glass were selected and a pin was placed at one of these points.
This is the first viewing pin.
Observation
 The observer was positioned at the level of the paper on the same side of the glass as the viewing pin,
 The observer aligned the viewing pin and the image of the stationary pin.
 A point on the paper was marked that was aligned with the viewing pin, the image of the stationary pin, and
the observer.
 This procedure was repeated for each of the other points selected for viewing pins.
Data Collection
 Lines were constructed between the stationary pin and each of the selected points (viewing pins)
 Lines were constructed between each of the selected points (viewing pins) and their corresponding marks of
observed alignment
 Normals were constructed relative to the edge of the glass at each of selected points (viewing pins).
 The angles relative to the normal on the glass side and the air side were measured
Results
Table 2.
Measured angles and calculated values of the index of refraction of glass. (nair = 1.0003)
Glass
Air
Selected Point
angle, θair
angle, θglass
index of refraction, nglass
A
B
C
D
Calculation of the index of refraction of glass, nglass, using data for the selected point A.
nglass  nair
sin air

sin  glass