What is Snell's Law?

Contributed by:

Jonathan James Fri, Jan 21, 2022 05:16 PM UTC

Reflection, Snell's law

1. Today’s agenda:
Introduction to Light.
You must develop a general understanding of what light is and how it behaves.
Reflection and Refraction (Snell’s Law).
You must be able to determine the path of light rays using the laws of reflection
and refraction.
Total Internal Reflection and Fiber Optics.
You must be able to determine the conditions under which total internal
reflection occurs, and apply total internal reflection to fiber optic and similar
materials.
Dispersion.
You must understand that the index of refraction of a material is wavelength-
dependent.

2. Light striking a surface may be reflected, transmitted,
or absorbed. Reflected light leaves the surface at the
same angle it was incident on the surface:
i = r
i r
Real Important Note: the angles are measured relative to the
surface normal.
Possible homework hint: the sum of the angles in a 4-sided polygon
is 360.

3. Reflection from
a smooth
surface is
(mirror- like).
Reflection from
a rough surface
is diffuse (not

4. Light travels in a straight
line except when it is
reflected or when it
moves from one medium
to another.
Refraction—the “bending,” or change of direction of
light rays when light moves from one medium to a
different one—takes place because light travels with
different speeds in different media.

5. The speed of light in a vacuum is c = 3x108 m/s. The
index of refraction of a material is defined by
c
n= , If you study light in advanced
classes, you’ll find it is more complex
v than this.
where c is the speed of light in a vacuum and v is the
speed of light in the material.
The speed and wavelength of light change when it
passes from one medium to another, but not the
frequency, so c 
v= and n = .
n n

6. Because light never travels faster than c, n  1.* For
water, n = 1.33 and for glass, n 1.5. Indices of
refraction for several materials are listed in your text.
Example: calculate the speed of light in diamond (n =
c
v =
n
3×108 m/s
v =
2.42
v = 1.24×108 m/s
*Actually, not true but don’t worry about it unless you take advanced courses in optics.

7. Because n  1, If n < 1, we
we see this: would see this:
Thanks to Dr. Xiaodong Yang for the
images.

8. Snell’s Law
When light moves from one medium into another, some
is reflected at the boundary, and some is transmitted.
The transmitted light is refracted (“bent”).
a is the angle of incidence, and b is the angle of
in re
ci fr
de ac
nt te
ra d
y a ra b
air (na) y air (nb)
water (nb) water (na)
b a
inc
ref
ide
ra
nt
cte
ray
d
nb>na na>nb
ray
na sin θa  = nb sin θb 

9. Light passing from air (n  1) into water (n  1.33).
Light “bends” towards the normal to the surface as
it slows down in water.
in
ci
de
nt
ra
y a
air (na)
(1)  sin θa   = (1.33)  sin θb  
water (nb)
θa > θb
b
ref
ra
cte
d
nb>na
ray
na sin θa  = nb sin θb 

10. Light passing from water (n  1.33) into air (n  1).
Light “bends” away from the normal to the surface
as it speeds up in air.
re
fr
ac
te
(1.33)  sin θa   = (1)  sin θb   d
ra
y
b
air (nb)
water (na)
θa < θb
a
inc
ide
nt
ray
na>nb
na sin θa  = nb sin θb 

11. Snell’s law, also called the law of refraction, gives the
relationship between angles and indices of refraction:
na sin θa  = nb sin θb  .
air (na) air (na)
a a
b b
water (nb) water (nb)
You are free to choose which is “a” and which is “b.”
 is the angle the ray makes with the normal!

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