More about Refraction

Refraction occurs because the speed of the light waves is different in each substance. The amount of refraction that takes place depends on the speed of the waves in each substance.

Consider a wavefront of a light wave when it passes across a straight boundary from a vacuum (or air) into a transparent substance. Suppose the wavefront moves from XY to X'Y' in time t, crossing the boundary between X and Y'. In this time, the wavefront moves:

• a distance ct at speed c in a vacuum from Y to Y'
• a distance cst at speed cs in the substance from X to X'

Considering traingle XYY', since YY' is the direction of the wavefront in the vacuum and is therefore  perpendicular to XY, then YY' = XY' sini, where i = angle YXY'.

ct = XY' sin i

Conesidering triangle **'Y', since **' is the direction of the wavefront in the substance and is therefore perpendicular to X'Y', then **' = XY', sinr, where r = angle XY'X'.

cst = XY' sinr

Combining these two equations therefore gives sini/sinr = c/cs

Therefore the refractive index of the subtance, n = c/cs

This equation shows that the smaller the speed of light is in a substance , the greater the reftractive index of the substance.

Consider a light ray crossing a boundary from a substance in which the speed of light is c1 to a substance in which the speed of light is c2.Using the same theory as on the previous card gives sini/sinr = c1/c2 where i is the angle between the incident ray and the normal and r is the angle between the refracted ray and the normal.

This equation may be rearranged as (1/c1)sini = (1/c2)sinr

Multiplying both sides of this equation by c, the speed of light in a vacuum, gives (c/c1)sini = (c/c2) sinr.

Substituing n1 for (c/c1) where n1 is the refractive index of substance 1, and n2 for (c/c2) where n2 is the refractive index of substance, gives Snell's Law: n1sinθ1 = n2sinθ2 where θ1 = i and θ2 = r.

The speed of light in air at atmospheric pressure is 99.97% of the speed of light in a vacuum.

Therefore, the refractive index of air is 1.0003. For most purposes, the refractive index of air may be assuemd to be 1.

We can use a prism to split a beam of white light from a filament lamp into the colours of the spectrum by a glas prism. This happens because white light is composed of light with a continuous ramnge of wavelengths., from red at about 650nm to violet at about 350nm. The glass prism refracts light by different amounts , depenmding on its wavelength. The shorter the wavelength in air, the greater the amount of refraction. So each colour in the white light beam is refracted by a different amount. This dispersive effect occurs because the speed of light in glass depends on wavelength. Violet light travels more slowly than red light in glass so the refractive index of violet light is greater than the refractive index of red light.