Reflection and Refraction
Physics 106
Concepts
1. What is light?
2. Reflection
3. Refraction
a. Snell’s Law
b. Index of Refraction
4. Dispersion
5. Total Internal Reflection
6. Polarization
Equations
c = 3 x 108 m/s
speed of light in vacuum c

speed of light in medium v
wavelength of light in vacuum 0

Index of refraction in terms of wavelength: n 
wavelength of light in medium n
Snell’s Law: n1 sin 1  n2 sin 2
Index of refraction in terms of velocity: n 
Total internal reflection: sin  c 
Polarization: tan  Brewsters 
n2
for n1  n2 , where θc is the critical angle.
n1
n2
for n1  n2
n1
45°
n=1.5
Calculate the critical angles for the following materials when surrounded by air when the
wavelength is 589 nm.
a. Zircon, n = 1.923
b. Fluorite, n = 1.434
c. Ice, n = 1.309
A cylindrical cistern, constructed below ground level, is 2.78 meters in diameter and 1.88
meters deep. It is filled to the brim with a liquid whose index of refraction is 1.56. A
small object rests on the bottom of the cistern at its center. How far from the edge of the
cistern can a girl whose eyes are 1.21 meters from the ground stand and still see the
object?
If red light of wavelength 700 nm in air enters glass with index of refraction 1.5, what is
the wavelength of the light in the glass?
A certain kind of glass has an index of refraction of 1.650 for blue light of wavelength
430 nm and an index of 1.615 for red light of wavelength 680 nm. If a beam containing
these two colors is incident at an angle of 30° on a piece of this glass, what is the angle
between the two beams inside the glass?
The lowest possible value for the index of refraction is:
a. 0.
b. 1.
c. 0.707.
d. 3-1/2.
A fish is 1.2 m beneath the surface of a still pond of water. At what maximum angle can
the fish look toward the surface (measured with respect to the normal to the surface) in
order to see a fisherman sitting on a distant bank? (for water, n = 1.333)
a. 18.6º
b. 37.2º
c. 48.6º
d. The fish will not see the fisherman at any angle.
Don’t worry about Huygens’s Principle!