Mammoth Memory

Different refractive indices

The refractive index is a ratio but it actually means that:

Refractive index `(n)` is the extent to which light is refracted (changes direction) when it enters a medium.

Also note that `n` is a constant for a particular medium.

Some examples are:

Refractive index table.

NOTE:  Low refractive index is low-density medium
   High refractive index is a high-density medium

 

So a high-refractive index `(n)` bends a lot more towards the normal line and a low refractive index `(n)` bends very little towards the normal line.

HIGH N° `n` = Much bend (HIGH bend) towards normal line
LOW N° `n` = Little bend (LOW bend) towards the normal line

Refraction of air to water `n=1.3`

Refraction of light travelling from air to water.

Refraction of air to glass `n=1.5`

Refraction of a ray of light as it travels from air into glass.

Refraction of air to diamond `n=2.4`

Refraction of a ray of light as it travels from air into diamond.

We can then use this information to find any angle of refraction when we know the value `n` (refractive index) and angle of incidence `(theta\i)` for any light ray travelling from air to a thicker medium.

`n=(sin\theta\i)/(sin\theta\r)`

Angle of incidence and angle of refraction of a ray of light.

 

Refraction of air to water

`n=1.3` and `theta\i=45^circ`

Angle of incidence and angle of refraction of a ray of light travelling from air into water.

`n=(sin\theta\i)/(sin\theta\r)`

`1.3=(sin45)/(sin\theta\r)`

divide both sides by 1.3 and multiply both sides by `sin\theta\r` to get `sin\theta\r` on its own.

`sin\theta\r=(sin45)/1.3`

`sin\theta\r=0.7071/1.3=0.5439`

`\theta\r=sin^(-1)\0.5439`

`\theta\r=32.95^circ~~33^circ`

 

Refraction of air to glass

`n=1.5` and `theta\i=45^circ`

 

`n=(sin\theta\i)/(sin\theta\r)`

`1.5=(sin45)/(sin\theta\r)`

divide both sides by 1.5 and multiply both sides by `sin\theta\r` we get:

`sin\theta\r=(sin45)/1.5`

`sin\theta\r=0.7071/1.5=0.4714`

`\theta\r=sin^(-1)\0.4714`

`\theta\r=28.12^circ~~28^circ`

 

Refraction of air to diamond

`n=2.4` and `theta\i=45^circ`

 

`n=(sin\theta\i)/(sin\theta\r)`

`2.4=(sin45)/(sin\theta\r)`

divide both sides by 2.4 and multiply both sides by `sin\theta\r` we get:

`sin\theta\r=(sin45)/2.4`

`sin\theta\r=0.7071/2.4=0.294`

`\theta\r=sin^(-1)\0.294`

`\theta\r=17.13^circ~~17^circ`

 

Summary

When light shines at 45° towards a surface the angle from the normal line to the refracted ray is:

  Water = 33°  
  Glass = 28°  
  Diamond = 17°  

 

Water 33°

Angle between normal line and refracted ray travelling into water.

 

Glass 28°

Angle between normal line and refracted ray travelling into glass.

 

Diamond 17°

Angle between normal line and refracted ray travelling into diamond.

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