# Refraction

When light passes from one medium to another of a different density, it changes direction. This bending of the lightbeam is known as refraction.
Refraction in a plexiglass block

When light passes from air to glass or water, it slows down. If it hits the medium interface at an angle, it changes direction. It is a bit like a car which comes off a road and hits grass or gravel. The car swerves and changes direction, because the pressure is applied unevenly and at different times to the two front wheels.

This phenomenon may be observed in a ripple tank, where water passes from one depth to another: the pressure changes, and the wavefronts change direction.

Refraction occurs when light passes from one medium to another. the angle of incidence is greater in the less dense medium.

# Snell's Law

Snell's Law relates the angle of refraction to the angle of incidence, with every substance having its own unique index of refraction (n)

Every material has its own refractive index (n). This is the degree to which light will be refracted when it passes from air through it. The refractive index of water is 1.33, and for glass or plexiglass it is about 1.5.

To calculate the angles of the light rays, we use the formula:

\$\$n = {sini}/{sinr}\$\$

where 'i' is the angle of incidence, and 'r' is the angle of refraction.

## Critical angle

Consider the situation where light is passing from a denser medium, such as water, to a less dense medium, such as air. Is there an angle of incidence where the angle of refraction is so great that the light does not pass into the air, but instead skims along the surface of the water?

In this case, r is 90°, so \${sinr} = sin(90) = 1\$

Snell's Law can be rearranged to find the angle of incidence. In the case of light passing from water to air, \$n = 1/{1.33}\$, so: \$sin(i) = 1/n⋅sin(r) = 1/{1.33}⋅1 = 0.75\$

\$i = sin^{-1}(0.75) = 48.75°\$

This is the critical angle - the angle of incidence which causes the light to skim along the surface of the medium.

Total internal reflection occurs when the angle of incidence is greater than the critical angle

Every translucent material will have its own refractive index (n). It is measured by Snell's Law: \$n = {sini}/{sinr}\$, where i is the angle of incidence, and r is the angle of refraction.

The refractive index is also the ratio of the speed of light in air/ speed of light in the medium.

Some indices of refraction

 vacuum = 1.00000000000 air = 1.00028 (STP) ice = 1.31 water = 1.3330 acetone = 1.36 ethanol = 1.36 teflon = 1.365 plexiglass = 1.4893 crown glass = 1.52 table salt (NaCl) = 1.544 PET* = 1.575 flint glass = 1.61 sapphire = 1.77 (average) diamond = 2.42 silicon = 3.96 germanium = 4.01

## Magnification

Objects are magnified when viewed in a different medium due to the refractive index.

### The Rainbow

When the white light of the Sun passes through water droplets suspended in the atmosphere shortly after rainfall, the light refracts just as it does in a prism, and the result is the spectacular rainbow.

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