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.
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!)
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.
Snell's law states that:
The absolute refractive index of a material is that compared to free
space which is given a refractive index of 1.000.
For light passing from one medium of
absolute refractive index n
1 to another of absolute refractive index n
2 the refractive index of the
interface is written as
1n
2.
The refractive index of the material also depends on the
wavelength of the radiation being considered. This relation is given by Cauchyts theorem:
The refractive index
of two different types of glass for three different wavelengths is given in the following table.
n
C 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 n
1 and n
2 respectively.
We have:
If the direction of the light is reversed:
Therefore:
2n
1 =
1/[
1n
2]
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
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
Wave
refraction
(a) a sloping beach
(b) a sudden depth
change
