Question

Question #1d195

Answer 1

The critical angle of a light ray, passing from a dense medium(glass) to a less dense medium(air), is angle angle at which the refracted ray is exactly `90^0`.

Now, all you do is to use Snell's law:

`n_gsini=n_asinr`

where `n_g` is the refractive index of glass
`n_a` is the refractive index of air
`i` is the angle of incidence
`r` is the angle of refraction

For critical angle `i` becomes `c`, and `r` becomes `90^0`
And we know that `n_a ~=1`

`=> n_gsinc=1`

`=>sinc=1/n_g`

`=> c=sin^-1(1/n_g)`

This could also be written as `c=sin^-1(v_g/v_(vac))`

Where `v_g` is the speed of light in glass
`v_(vac)` is the speed of light in a vacuum or air.