The Refraction of Light : Notes/W.S.-10
When waves enter a different medium, they may speed up or slow
down. The direction of the waves will then change. This change in
direction is called refraction. The refracted beam bends towards or
away from the normal, depending on whether the beam slows down or
speeds up.
For example, when light moves from air to water, it slows down and the
light bends towards the normal.
air
water
Using geometry, we can derive an important formula. The incident and
refracted wave fronts are shown below.
incident
wavelength
angle of
incidence
i
a
angle of
refraction
R
b
refracted
wavelength
In the diagram above, the light wave slows down so that the wavelength
decreases. Therefore, we have:
λ incident
ab
= sin ( i)
and
λ refracted
ab
= sin ( R )
Since the frequency doesn't change, we also have:
vi
vR
=
λi
λR
The above equations combine to give Snell's Law for light traveling
from air to a more dense medium.
sin(i) vi
=
=n
sin(R) vR
The ratio of the velocity of light in air to the velocity of light in the
dense medium is called the index of refraction. It is given by the
symbol n.
For a light beam traveling from the dense medium to air, Snell's Law
becomes:
sin(i) 1
=
sin(R) n
Problems:
1)a) The speed of light in a vacuum (or air) is 3.00x108 m/s. When
light enters water from the air, it slows down to 2.26x108 m/s. Find
the index of refraction for water.
b) If the angle of incidence (i) equals 38.0°, find the angle of refraction.
i
air
water
R
2)a) An incident light ray enters water from the air. If the wavelength
of the light in air is 5.0x10-7 m, find the frequency.
(use v = f⋅ λ )
b) Find the wavelength of the refracted beam.
c) Find the frequency of the refracted beam.
3) If the index of refraction (n) for a substance is equal to 1.5, what
will the speed of light in that substance be?
4) The index of refraction for diamond is 2.42. Fill in the blanks.
angle of incidence i
angle of refraction R
25.0°
____
56.0°
____
____
15.0°
____
0.0°
5) The angle of incidence i equals 32.0°, and the angle of refraction R is
found to be 22.0° for a certain type of plastic.
i) Find the index of refraction.
ii) Find the velocity of light in the plastic.
6) If a light ray enters the air from water, the ray bends away from
the normal as shown below. Find the angle of refraction R.
air
R
water
28.0
7) Draw a picture to show what happens to the light ray as it goes
through the pane of glass. (use a pencil and ruler)
ray
air
glass
air
Answers: 1)a) 1.33, b) 27.6°, 2)a) 6.0x1014 Hz, b) 3.8x10-7 m, c)
6.0x10 14 Hz, 3) 2.0x108 m/s, 4) 10.1, 38.8, 20.0, 0.0, 5)i) 1.41, ii)
2.12x10 8 m/s, 6) 38.6°, 7)
ray
air
glass
air