Physics
Refraction Investigation
Snell's Law Derivation
When light travels from air into water or glass the path of the light is bent. This bending of light
as it goes from one substance into another at an angle is known as refraction. In this
investigation we will measure the angle through which a light ray is bent as it passes from air into
water. The purpose of this investigation is to derive a mathematical relationship between the
angle of incidence and the angle of refraction.
Equipment:
1 piece of cardboard
1 piece of polar graph paper
1 semi-circular plastic water dish half full of water
2 stick pins
1 graphing calculator or piece of rectangular graph paper and regular calculator
Procedure:
1.
Place the polar graph paper on the cardboard. Place the water dish so the long flat edge is
flush with the 90°-270° line with the scratch (look for the scratch at the center of the long
side of the dish) aligned with the center cross hairs on the graph paper (see diagram
below).
2.
Stick one pin in the graph paper on the flat side of the dish about an inch or so from the
dish along the 0°-180° line as shown in the diagram above (make sure the pin is vertical).
You must now think of a light ray leaving the pin you just put in and traveling to the
scratch in the dish and entering the water at that point. The angle of incidence for this case
is 0°.
3.
Now look through the dish of water (so you have to get down and look in just above
table top level) from the curved side. Close one eye and move your head from side to side
looking for the image of the pin through the water. Do you see the image of the pin? Now
line up the image of the pin you see with the image of the scratch in the center of the dish.
Place a second pin vertically in the cardboard on the curved side of the dish so that it covers
up the image of the first pin and the scratch that you see through the water. You should
find the second pin is on the 0°-180° line (it doesn't matter how far from the curved side of
the dish). If it is not on this line, check the alignment of the dish as described in #1 above.
4.
Now move the first pin (on the straight side of the dish) to the left 10°. The 10° is defined
as the angle of incidence (i) for the light ray in this case. Remove the second pin on the
curved side of the dish and look through the water again with one eye closed. Line up the
image of the first pin and the image of the scratch as seen through the water, then poke the
second pin in the graph paper on the curved side of the dish so it again lines up with the
two images. You should find that the location of the second pin has moved to the right
from its previous position on the order of 7.5° or so. Record the angle of refraction, r, (the
angle from the 0°-180° line) in the chart below.
5.
Repeat step 4 increasing by 10° each trial up to an angle of incidence of 50° (60° might be
too hard to see clearly).
i (°)
r (°)
sin(i)
sin(r)
sin(i)/sin(r)
0
0
0
0
n/a
10
20
30
40
50
6.
After you have recorded the angles of refraction, use a calculator and fill in the rest of the
table.
Data Analysis
1.
On your calculator (or on a piece of rectangular graph paper), plot sin(i) on the y-axis and
sin(r) on the x-axis (yes, I know that's backwards according to proper science practices, but
do it anyway).
2.
Do a linear regression on the calculator (or draw in the best fit straight line on the graph
paper and measure the slope) to determine the equation for the best fit straight line through
your data. Instead of writing y=mx+b, you substitute "y" in the equation for "sin(i)" and
"x" for "sin(r)" and the value of m from your calculator (or calculations). Hopefully the yintercept is minimal and can be ignored.
3.
Take an average of the last column to the right on your chart above (ignoring 0° of
incidence). Is this average close to the slope you calculated?
Conclusion
Write the final equation (also called an "expression") which describes the behavior of a light ray
as it enters water from air in the space below (we are ignoring the plastic in this investigation don't worry, it is legal). This expression is known as Snell's Law of Refraction.