Snell’s law
Equipment: The experiment consist of a laser ray box, optics bench, 2 beakers, 2 circular cartesian
coordinate ray trace table, roll of paper towel, hand sanitizer, 2 refraction cups, red desk lamp,
acrylic lenses, right angle triangle lense, parallel ray bar lense, meter stick, Laser safety goggles,
water, glycerin, and protractor.
PRECAUTION!!
This experiment uses a laser ray box. Do not let the laser beams or its reflections strike your
eyes. Also, watch out for the laser beams from other lab benches! People (sometime) don’t always
look before they put the laser ray box on. Be cautious and use your goggles!!
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Purpose
Observe and measure the effects of light transmission and refraction through various substances.
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2.1
Theory
Index Of Refraction
You will be observing the effects of light being bent as it enters various mediums. This is defined
as refracted light. The refracted light you observe will be propagating through various materials
at speeds slower then c. Light waves that propagate through the various materials will slow down
and this will cause the beam of light to bend in the material.
The angle of bend varies on the index of refraction. Below is a table indicating the index of
refraction of various materials.
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General Physics II
Lab: Snells law
Medium
Vacuum
Air
Water
Acrylic glass
Ethyl Alcohol
Crown glass
Plexiglass
Glycerol
n
1
1.00029
1.33
1.49
1.36
1.52
1.51
1.4729
Keep in mind the index of refraction of any material varies on temperature, pressure, and the
wavelength of the light source. Typically light that is in the 400 nm range will deflect at a higher
index of refraction then light that is in the 700 nm range. The table above list the index of refraction
those various materials at around 589 nm.
2.2
Snell’s Law
In vacuum light is regarded to travel approximately at 2.99 x 108 m/s. Which is defined as c.
When light propagates through various materials it will travel at a velocity v less than the speed
of light. To calculate the index of refraction of the material that light is passaging through use the
ratio of (c/v). The initial velocity is defined as c and the velocity that light is traveling through
the material which is v. The index of refraction of the material is given by the relatioship between
c and v.
n = c/v
(1)
When light enters from one material to the next it will take a path that is dictated by Snell’s
law. The angle of the bend is determined by the index of refraction of the material. Again, the
bending of the beam of light in the material is called refraction. Snell’s law states the following.
n1 sinθ1 = n2 sinθ2
(2)
The n1 indicates the index of refraction and θ1 the angle of the initial beam of light with respect
to the normal on the surface of the second medium. The n1 and θ1 are the index of refraction of
the material and the angle of light entering into the second medium. (In this case we’re labeling
the second medium n2 .) When light rays enters a medium with a higher index of refraction. The
ray of light in the higher index of refraction will bend toward normal line on the incident surface.
The opposite will occur if the rays of light going from a medium of a higher index to a lower index.
That is when n2 > n1 .
2.3
Critcal Angle and Total Internal Reflection
At the critical angle all the light at the intersection will bend parallel to the surface. This means
none of the light passes to the next medium. Once past critical angle total internal reflection
occurs. The ray of light travels from a medium with a high index of refraction to a medium with a
lower index of refraction greater then critical angle θc .This occurs when the incident angle is equal
or greater than the critical angle. The critical angle is determined by the ratio of initial index of
refraction over the final index of refraction. Below are images of critical angle and total internal
reflection. Equation 3 represents critcal angle.
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General Physics II
Lab: Snells law
sinθc = nf /ni
3
3.1
(3)
The Experiments
Equipment Arrangement and seeing Refraction
On your bench you should see an optical track that has two optical table mounts and a white screen
all mounted in one dimension. Mount the laser ray box on top of the outer table mount. The laser
ray box can produce one, three, or five laser beams at once. In this part we will use the single
beam and three beam output.
Set up the laser ray box on top of the outer table mount. Make sure the front of the ray box
runs perfectly along the center of the ”NORMAL” line on the round table mount. Place your
goggles on and turn on the ray box. Select single beam output. Check the laser beam path and
make sure that the laser beam runs straight through the center of the following table mount into
the center of the white screen. The beam should be parallel to the ”NORMAL” line of the of the
round table mount. Look at the following image.
3.2
Observing Refraction
Next mount the rectangular shaped parallel bar on the other round table. Align the parallel bar,
so that the beam going through the bar runs through the center of the NORMAL line on the ray
table. Make sure that its side runs perfectly parallel to the 0 degree line on the round table mount.
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General Physics II
Lab: Snells law
Data: Using the turntable rotate the acrylic glass parallel bar at the following angles below.
Calculate the index of refraction at each angle. Also, pick three other incident angles, below 60
degrees. Measure the angles of refraction by looking through the acrylic glass parallel bar and using
the small circular scale, then calculate n. Keep in mind that the measurement of refraction angle
is not exact. The small circular scale of measurement for refraction are in 5 degree increments, so
pick good incident angles.
Angle of Incidence
15◦
22◦
30◦
Angle of refraction
Questions:
(1) What starts to occur to the incident beam when you go beyond 60◦ ?
(2) Explain what is occurring to the beam inside the parallel bar?
(3) Why can your data be off?
(4) Is it possible to obtain total internal reflection?
3.3
Observing total internal reflection
Remove the parallel bar. Realign the optical ray table as in previous section and set the laser ray
box to three beam output. Take the right angle triangle and mount it so that all three beams
experience total internal reflection. Explain your observations.
Questions:
(1) How did you arrange the triangle on the round ray table?
(2) What angle did you use and why?
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General Physics II
3.4
Lab: Snells law
Determining the index of refraction of different liquids
Note: The beakers, and the 2 refraction cups are labeled, so try not to cross contaminate the fluids! In this part of the experiment we will use the refraction cup. Realign the laser
with the ray table and switch the laser ray box to single beam output. Align the refraction cup so
that the incident beam is hitting the center of the flat side of the cup. The flat side of the refraction
should be perfectly to the normal axis on the ray table. Use the pipette and fill the refraction cup
with water all the way to the top.
Measure the angles of refraction at the following angles, then using equation 2 you will calculate
the index of refraction of water. When you are done with water empty the refraction cup into the
correct beaker. Use the second refraction cup labeled glycerin and fill it up with glycerin. Repeat
as you have done before.
Angle of Incidence
15◦
22◦
30◦
39◦
50◦
Angle of refraction
Questions:
(1) How would you calculate the index of refraction if you reverse the direction of the dish so that
the incident ray is hitting the curved side of the refraction cup instead of the flat side?
3.5
Critical angle
This time you will setup the refraction cup so that the laser beam strikes the curved side of the
cup. Fill the refraction cup to the top with water. Center and align the refraction cup so that the
beam runs through the center of the refraction cup.
Next, increase the angle of the refraction cup so that the refracted ray starts to runs parallel
to the straight side. This is critical angle. Compare your experimental results to the theoretical
value. You can calculate the theoretical value using equation 3.
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General Physics II
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Lab: Snells law
Comment
Be considerate for your fellow humans and empty the refraction cups out into the proper beakers.
Wipe the refraction cups, round table, and the top of the bench dry. Place all the equipment back
in proper order. If not your TA will take off points. Cheers!
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