REFRACTION
For a simple introduction to refraction look at the Refraction file in the 11-14 section.
(See: 11-14/Light/Text/Refraction)
When light waves pass from air into a more dense material such as water, glass, plastic etc.
they slow down.
The ratio of their velocity in air (or more correctly in free space) to their velocity in the material is
called its refractive index.
Refractive index = velocity in free space (usually taken as air)
velocity in the material
The table below shows the refractive indices of some common substances. One of the reasons
why diamonds sparkle is partly connected with their high refractive index (their shape also has
something to do with it!)
Material
Diamond
Ruby
Duodomethane
Carbon disulphide
Glass (flint)
Glass (crown)
Refractive index
2.42
1.76
1.74
1.63
1.53-1.96
1.48-1.61
Refractive index
1.47
1.38
1.33
1.31
1.000 298
Glycerol
Magnesium fluoride
Water
Ice
Air at STP
Note the magnesium fluoride – this is used in non-reflecting coatings, blooming of lenses).
The change of velocity when light moves from one medium to another gives a change of
direction when the beam hits the boundary at an angle. When the light travels from a less dense
material such as air into more dense material such as glass it bends towards the normal,
bending away from the normal when its direction is reversed.
The law relating the angle of incidence (i), the angle of
refraction (r) and the refractive index (n) was discovered in
1621 by Willebrod Snell and is therefore known as Snell's
Law.
normal
angle of
incidence
i
Snell's law states that:
Refractive index (n) = sin i/sin r
r
The absolute refractive index of a material is that
compared to free space which is given a refractive index of
1.000.
Figure 1
angle of
refraction
1
For light passing from one medium of absolute refractive index n1 to another of absolute
refractive index n2 the refractive index of the interface is written as 1n2.
The refractive index of the material also depends on the wavelength of the radiation being
considered. This relation is given by Cauchy’s theorem:
Cauchy’s formula:
n = 1 + A/2
The refractive index of two different types of glass for three different wavelengths is given in the
following table.
Type of glass nC
nD
nF
Crown glass
1.5150 1.5175 1.5233
Flint glass
1.6434 1.6550 1.6648
nC is the refractive index for the C line of hydrogen wavelength 656 nm
nD is the refractive index for the F line of hydrogen wavelength 589 nm
nF is the refractive index for the F line of hydrogen wavelength 486 nm
(See also: 16-19/Optics/Refraction/Text/Achromatic prisms and lenses)
Light passing from one transparent material to another
Consider a beam of light passing from material 1 to material 2. (Figure 2) Let the absolute
refractive indices of the materials be n1 and n2 respectively.
We have:
1n2
= sin 1/sin2
If the direction of the light is reversed
2n1
Therefore:
2n1
= sin 2/sin1
= 1/[1n2]
Notice that we have made an important assumption here, namely
that the light will follow the same path whether it is travelling in one
direction or the other. This is known as the principle of reversibility
of light.
If the refractive index for light going from air to glass is 1.5 then if
the light is traveling from glass to air the refractive index would be
1/1.5 = 0.67

material 1
material 2
 
Figure 3
2
Velocity considerations
When light passes from one transparent material to another of different refractive index its
speed changes. The ratio of the speeds in the two materials is the inverse ratio of the refractive
indices of the two materials
c1/c2 = n2/n1 = sin1/sin2
or n1c1 = n2c2
Example problem
Speed of light in water = 2.26x108 ms-1 Speed of light in diamond = 1.25x108 ms-1
c1/c2 = sin1/sin2
Consider a ray of light meeting a water/diamond interface at 30o to the normal. Angle of refraction is
given by: sin2 = sin30 x 1.25x108/2.26x108 = 0.5x0.55 = 0.275
Therefore 2 = 16o
Wave refraction
(a) a sloping beach
(b) a sudden depth change
Shallow water
Shallow water
Deep water
Deep water
Shallow water
Figure 4
Shallow water
3