Critical angle

When light passes from one medium (material) to another it changes speed. This is because the speed of a wave is determined by the medium through which it is passing.

When light speeds up as it passes from one material to another, the angle of refraction is bigger than the angle of incidence.

For example, this happens when light passes from water to air or from glass to water.

$Light passing from water to air - there is a dotted line which runs perpendicular to the air and water interface. This is the 'normal'. The angle of incidence is the angle between the light (in water) and the normal, and the angle of refraction is the angle between the light (in air) and the normal.$

The diagram above shows light incident on a water-air interface.

Angle of incidence is the angle between an incident ray and the normal.
Angle of refraction is the angle between a refracted ray and the normal.

Angle of refraction less than 90 degrees

$Angle of refraction less than 90 degrees passing between glass and air - the angle of the ray of light is slightly deflected as it travels into the air.$

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At the interface between two materials, the angle of refraction cannot be greater than 90°. Click above to see what happens as the angle of incidence gets bigger.

When the angle of refraction is equal to 90°, the angle of incidence is called the critical angle, $\theta _c$

At any angle of incidence greater than the critical angle, the light cannot pass through the surface - it is all reflected.

This is called total internal reflection.

Total because all of the energy is reflected.
Internal because the energy stays inside the material.
Reflection because the light is reflected.

The relationship between critical angle and refractive index is $\sin \theta _c = {1 \over n}$

Question

Calculate the critical angle for red light incident on a water-air interface.

The refractive index of water is 1.33 for this colour of light.

Answer

$\eqalign{ n &=& 1.33 \cr \cr \sin \theta _c &=& {1 \over n} \cr \cr \sin \theta _c &=& {1 \over {1 \cdot 33}} \cr \cr \theta _c &=& 48.7535^ \circ \cr}$

Critical angle of water for this light = 48.8°

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Critical angle

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Critical angle

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