Download index of refraction

INDEX OF REFRACTION
Objective:
To verify Snell’s Law of Refraction by measuring the index of refraction for water and glass.
Equipment:
plastic reservoir, cardboard, straight pins, ruler, protractor, unlined paper, glass prism.
Introduction:
When light is incident on a surface, it has two options. It can be reflected off the surface, meaning
that it will “bounce” off the surface, or it can pass through the medium, being refracted. Usually
some of both phenomena will occur.
If the incident light is striking the surface at some angle with the normal (line perpendicular to the
surface), then the reflected and refracted light will be at angles with the normal. The reflected light
will make an angle with the normal equal to the incident angle. This seems normal to us when we
think of billiard balls striking the sides of the pool table. However, less familiar is the phenomenon
of refraction. When the light strikes the medium, it changes velocity. This causes a change in
direction of the light ray. The light bends, but it bends only at the surface. The velocity of the light
is dependent on the index of refraction of the material, n, so that
v=c/n
(1)
where c is the speed of light in a vacuum and v is the velocity of light in the medium.
If the light is passing from one medium into
another where the velocity is slower, the
light will be refracted towards the normal to
the surface. If the light is moving to a
medium when the velocity is higher, the light
is refracted away from the normal.
s2
h2
In a geometrical sense, the index of
refraction is easily determined by use of an
empirical equation known as Snell’s Law,
n1sin(1) = n2sin(2)
(2)
Snell’s Law
Where n1 is the index of refraction for the
medium of the incident light, a is the incident
angle, n2 is the index of refraction of the
material that the light is entering, and b is the
angle of refraction. According to this law, if
the angle of incidence is changed then the
angle of refraction must change in such a
way that the ratio of the sines of the two
angles will remain constant.
h1
normal
s2
Figure 1
The physical explanation of Snell’s Law is that the index is the ratio of the speeds of light in the
two media. Therefore,
n2
sin 1
v

 1
n1 sin  2 v 2
When determining the index of refraction of a material it is the ration of the spped of light in free
space to the speed of light in the material. Since the speed of light in air is very close to that in
free space, we can define the index of refraction of a material as the ratio of the speed of light in
air to the speed in the material, nfree space = nair = 1.
Procedure
Part A:
Lightly pin a piece of clean unlined paper to the cardboard. Place the empty plastic reservoir in
the center of the paper. Trace around the reservoir so that you will be able to measure angles
later. It also helps when repositioning the tray. Remove the reservoir.
At the center of the flat edge, draw a straight line perpendicular to the flat edge, all the way
through the other side of the reservoir’s outline. This line is the normal to the surface where the
light will be refracted. Next draw a line away from the center of the flat side such that it makes a
30 angle with the normal line. (See h1 in figure 1.) This line will represent the incident ray. Then
fill the water reservoir about two-thirds full with water and place it exactly on the outline.
Insert a straight pin vertically on the incident ray a modest distance away from the tray. Place
another straight pin on the line. You may place one of the pins at the center where the normal
meets the outline’s flat surface. Next view the two pins from the curved side of the reservoir,
being sure that you’re looking through the water. Line the two pins up so that they seem to lie in a
straight line. (Remember to use only one eye. This doesn’t work with binocular vision as each eye
sees a different line.) Now, visually align another pin with the images of the first two, between your
eye and the reservoir, so that all three seem to be in a straight line. You will have two pins on the
flat side and one pin on the curved side.
Remove the water reservoir and the pins. The line through the two pinholes on the flat side to the
edge of the outline of the reservoir represents the incident ray. Draw a line perpendicular to the
normal from one of the pinholes on the incident side, making a right triangle. See figure 1.
On the exit side of the reservoir, draw a line from the single pinhole through the outline of the
reservoir to the center of the flat edge. This represents the exit ray. (Note that we are drawing
many of our lines through this center spot!) Draw a line perpendicular to the normal from the
pinhole on the exit side, making another right triangle. See figure 1.
Measure the hypotenuse, h, and the short side, s, of each right triangle. Record the lengths. The
sine of the angle will be the quotient of the two.
Repeat the above procedure using incident angles of approximately 40 and 50.
Using Snell’s Law, find the index of refraction of the water for each incident angle. The sines of
the angles may be found without actually finding the values of the angles themselves. The index
of refraction will be given as:
n = (h2s1)/(h1s2)
Where the subscript 1 indicates the incident side and the subscript 2 indicates the exit side.
Find the average index of refraction and standard deviation and record this as your experimental
value.
Compare your experimental value with the standard value of 1.33 by calculating the percent error.
%err = [abs(nexpeimental – nstandard) / nstandard ]  100%
Using Equation 1, find the velocity of light in water.