12.4 The Index of
Refraction
Recall...
• Last class, w e discussed that
light bends (refracts) w hen it
goes from one medium
(substance) to another.
Index of Refraction
Index of refraction is represented by the letter --> n
‘n’ is a value given to a medium based on how much is slows
down the speed of light…
As the value of n increases, the speed of light
decreases... Meaning the light will bend
more
Ex: Diamonds slow down (bend) light more
than water, thus diamonds have a greater
index of refraction than water
Common Values
Light in vacuum n= 1.00
Light in air n= 1.0003 ~ 1.00
Light in water n= 1.33
How are these values obtained?
The Index of Refraction of Material is found by
comparing the speed of light in their respective
mediums
The Index of Refraction for Various Media
As the value of n increases, the speed of light decreases...
Light bends more
Medium
Index of
Refraction
Medium
Index of
Refraction
air/ vacuum
1.00
vegetable oil
1.47
ice
1.31
olive oil
1.48
pure w ater
1.33
acrylic
1.49
ethyl alcohol
1.36
glass
1.52
quartz
1.46
diamond
2.42
How Does Light Bend?
Speed of light in
air
3.00 x 108m/sec
Speed of light in
water
2.26 x108m/sec
Remember...
Light bends TOWARD the normal when the
speed of light in the second medium is less than
the speed of light in the first medium. (Light
bends TOWARDS the normal when entering a
more dense medium)
How Does Light Bend?
Speed of light in
air
3.00 x 108m/sec
Less Dense
2nd
Medium
Air
Water
Speed of light in
water
2.26 x108m/sec
1st
Medium
More Dense
Light bends AWAY from the normal when the speed of light in
the second medium is GREATER.In other words...Light bends
AWAY from the normal when entering a less dense medium
INDEX OF REFRACTION
• The ratio of the speed of light in a vacuum to
the speed of light in a medium
• Equation:
c
n= v
n = index of refraction*
units = m/s
c = speed of light
v = speed of light in given medium
*n does not have units: units from c and v cancel out
INDEX OF REFRACTION
• The index of refraction can be calculated using
the sines of angles.
n=
sin∠i /(θi)
sin∠R /(θr)
∠i or (θi) is the angle of incidence and
∠R or (θr) is the angle of reflection
Where
How to Calculate the Index of Refraction
Sample Problem 1
• The speed of light in sodium chloride (salt) is
1.96 x 108 m/ s. Calculate the index of refraction
for sodium chloride.
• Use G.R.A .S.S. M ethod
• Given: c = 3.00 x 108 m/ s; v sodium chloride = 1.96 x
108 m/ s
• Required: n = ?
• A nalysis =
• Solution = 3.00 x 108 m/s
8
1.96 x 10
= 1.53
m/s
NO UNITS!!!
Statement = The index of refraction for sodium
chloride (salt) is about 1.53
Calculating the Speed of Light
SAMPLE PROBLEM 2
• Calculate the speed of light in olive oil
• What is the first step???
Given
• c = 3.00 x
8
10
m/ s (speed of light in a vacuum)
• noliveoil = 1.48 (from table on page 524)
• N ext...
Required
• v = the speed of light in olive oil
• N ext...
Analysis & Solution
c
n= v
c
v =
n
Next...
vxn = c
v =
v =
3.00 x
8
10
m/s
1.48
8
2.03 x 10 m/s
Sentence
• Therefore, the speed in olive oil is about
8
2.03 x 10 m/ s
c
v =
n
n = index of refraction
c = speed of light
(3.00x108m/s)
v = speed of light in given medium
Page 525 #1-7
• 1. a) The index of refraction for a medium is the
ratio of the speed of light in a vacuum to the
speed of light in that medium.
• b) The index of refraction is a dimensionless
quantity because it is the ratio of tw o speeds,
w hich both have the same units. The common
units in the numerator and denominator of the
ratio cancel, leaving no units for the index of
refraction.
2.
nvinegar =
3.
nsapphire =
3.00 x
8
10
m/s
2.30 x
8
10
m/s
3.00 x
8
10
m/s
1.69 x 108 m/s
=
1.30
=
1.78
4.a)
vquarts =
4.b)
vquarts =
3.00 x
8
10
m/s
1.46
3.00 x
8
10
2.42
m/s
=
2.05 x 108 m/s
=
1.24 x 108 m/s
5.
vsolution =
6.
vacetone =
3.00 x
8
10
m/s
1.49
3.00 x
8
10
1.36
m/s
=
=
2.01 x 108 m/s
2.21 x
8
10
m/s
7.a)
nunknown=
3.00 x 108 m/s
2.20 x
8
10
m/s
7.b) Ethyl alcohol or acetone
=
1.36
Phenomena Related to Refraction
Water on Pavement
M any people have noticed
w hat appears to be a pool of
w ater in front of them as
they drive along a highw ay.
 The pool of w ater seems to
be only a short distance
aw ay, yet the car never
seems to reach it.
 The pool seems to be
constantly moving aw ay.

Mirage
a virtual image that
forms as a result of
refraction and total
internal reflection in
Earth’s atmosphere
A mirage can appear when light is travelling from cool
air to warmer air.