Refraction: Snell's Law
When light passes from one medium to
another medium it
changes its direction.
We call this change in the direction of
light refraction
The amount of refraction by using the
refractive indexes of the mediums.
n=c
vmedium
ratio of the speed of light in vacuum to
the speed of the light in given medium.
Index of Refraction
ratio between the speed of light in a vacuum and speed of light in a n = cv
trasparent medium
c = speed of light in a vacuum
v = speed of light in a medium
n = index of refraction (the ratio)
V air is 3.00x108
n = c/v = 1
air offers very little resistance.
However: when light travels through
water, for example, it slows down.
The light bends toward the normal when it
enters a medium that is more dense,
Table of indices of Refraction
page 61 of old text
Example: Speed of light in a liquid is 2.25 x 108 m/s.
What is the a) refractive index of the liquid?
a) c = 3.00 x 108 m/s, v = 2.25 x 108 m/s
Formula: n = c/v
Calculation: n = 3.00 x 108 m/s/2.25 x 108 m/s = 1.33
b) look on page 61 of text, what is the liquid according to the
table of indices of Refraction?
Snell's law is written
n sinθ = n sinθ
1
i
2
R
n is the index of refraction for the
1
first medium
n is the index of refraction for the
2
second medium
Use subscripts to indicate the different mediums.
Example
Light travels from crown glass (g) into water (w). The angle of
o.
incidence in crown glass is 40.0 What is the angle of
refraction in water?
(use the table to get indices of refraction p.61)
n gsinθg = n wsinθR
o
1.52 sin 40.0 = 1.33 sinθR
sinθw = (1.52)(0.643)/1.33 = 0.735
-1
θw = Sin (0.735)
o
θw = 47.3
Total Internal Reflection and the Critical Angle
As the angle of incidence increases, the intensity of a
reflected ray becomes progressively stronger. And...
intensity of a refracted ray becomes progressively weaker
until there is no refraction only reflection.
θ
R
θr
θi
Total internal reflection ­ occurs when light is leaving a denser medium and is travelling into a less dense medium and
θ > the critical angle. i
N
Total internal reflection The critical angle is a constant between two media. ­ occurs when light is leaving a denser medium θi when θR = 90
It is the value of o
and is travelling into a less dense medium and
a) θi < the critcial angle : a refracted ray (partial reflection). θ > the critical angle. b) θii = the critical angle : critical ray of 90o(to the normal). c) θi > the critical angle : totally reflected ray (no refraction)
To calculate the critical angle Total internal reflection
for any substance set the angle of refraction to 90o . ­ occurs when light is leaving a denser medium = 2.42) to air (n = 1.0003) Example: The light ray is travelling from diamond (n
and is travelling into a less
dense medium and
1
2
n1sin ic = n2 sin R θ
. = n sinθR
n1 > i 2
i sinθthe critical angle
o
2.42 (sinθ ) = 1.0003 (sin 90 ) i
2.42 (sin θ ) = 1.0003 (1.0) i
2.42(sin θ ) = 1.0003 i
­1
sin θ = 0.4133 θ = sin (0.4133) i = 24.4o i
i Practice in textbook
P. 78‐79 # 16, 17, 23, 30, 36, 37, 38, 39, 40,42,45, 50 (3 mediums therefore 2 steps)
Note the answers to many of the questions are in the back.