An Introduction to Refraction
SNC2D
Index of Refraction
Light will travel more slowly in more dense
materials. The ratio of the speed of
light in a vacuum (or air) to the speed in
the material is the index of refraction
(or refractive index), n.
c
n
v
Index of Refraction: Example
For water, the index of refraction is 1.33.
The speed of light in water is therefore:
G : n  1.33
c  3.0 108
U :v  ?
m
s
Index of Refraction: Example
For water, the index of refraction is 1.33.
The speed of light in water is therefore:
G : n  1.33
c  3.0 108
U :v  ?
m
s
c
c
S :n   v 
v
n
Index of Refraction: Example
For water, the index of refraction is 1.33.
The speed of light in water is therefore:
G : n  1.33
c  3.0 108
U :v  ?
m
s
c
c
S :n   v 
v
n
3.0  108 ms
S :v 
 2.3 108
1.33
m
s
Frequency and Wavelength
Since the wave slows down
but the frequency remains
the same (the frequency of
a wave is always the
frequency of the source),
the wavelength gets
shorter.
v
v  f   
f
Boundaries
So in 2D (with the boundary at an
angle to the wave), the wave will
bend as those parts that enter
the more-dense material first
slow down first.
(The black lines show the crests or
“wavefronts”).
Please Note!
If the ray is perpendicular to the boundary,
no bending will occur:
Snell’s Law
The amount by which the wave is bent is
given by Snell’s Law (ni and nr are the
refractive indices of the media).
ni sin i  nr sin r
Snell’s Law
Note that a ray will always bend towards the
normal when travelling into a more-dense
medium
Snell’s Law
Note that a ray will always bend towards the
normal when travelling into a more-dense
medium (and away from the normal when
travelling into a less-dense medium).
Problem Solving with Snell’s
Law
When light passes from air into water at an
angle of 45o from the normal, what is the
angle of refraction in the water?
Problem Solving with Snell’s
Law
When light passes from air into water at an
angle of 45o from the normal, what is the
angle of refraction in the water?
G : nair  1.0
nwater  1.33
 air  45
U :  water  ?
Problem Solving with Snell’s
Law
When light passes from air into water at an
angle of 45o from the normal, what is the
angle of refraction in the water?
G : nair  1.0
nwater  1.33
 air  45
U :  water  ?
S : nair sin  air  nwater sin  water
 sin  water
nair sin  air

nwater
Problem Solving with Snell’s
Law
When light passes from air into water at an
angle of 45o from the normal, what is the
angle of refraction in the water?
G : nair  1.0
nwater  1.33
 air  45
U :  water  ?
S : nair sin  air  nwater sin  water
 sin  water
nair sin  air

nwater
Problem Solving with Snell’s
Law
When light passes from air into water at an
angle of 45o from the normal, what is the
angle of refraction in the water?
G : nair  1.0
nwater  1.33
 air  45
U :  water  ?
S : nair sin  air  nwater sin  water
 sin  water
nair sin  air

nwater
(1.0) sin 45
S : sin  water 
 0.53166
1.33
 water  sin 1 (0.53166)  32
Problem Solving with Snell’s
Law
When light passes from air into water at an
angle of 45o from the normal, what is the
angle of refraction in the water?
G : nair  1.0
nwater  1.33
 air  45
U :  water  ?
S : nair sin  air  nwater sin  water
 sin  water
nair sin  air

nwater
(1.0) sin 45
S : sin  water 
 0.53166
1.33
 water  sin 1 (0.53166)  32
Dispersion
Note that since different
wavelengths of white
light refract slightly
differently, refraction
can split white light into
its different wavelengths
(i.e. colours) especially
if refracted twice.
Dispersion
Note that since different
wavelengths of white
light refract slightly
differently, refraction
can split white light into
its different wavelengths
(i.e. colours) especially
if refracted twice.
Dispersion
Note that since different
wavelengths of white
light refract slightly
differently, refraction
can split white light into
its different wavelengths
(i.e. colours) especially
if refracted twice.
This is called dispersion.
More Practice
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p. 438 Practice Problems 1-3 (top set)
p. 441 Practice Problems 1-3
p. 442 Practice Problems 1-3