Question

Determine whether light traveling from diamond (refractive index 2.42)to air,reach air if it approaches at angle (i)65.6° (ii)34.4° (iii)74.4° to glass top surface?

Answer 1

The light does not reach the air in any of these cases.

It can reach air only for angles of incidence roughly less than `24.4º`

Explanation:

Given that the light rays are passing from a dense medium(diamond) to a less dense medium(air), there is a possibility of it being totally internally reflected, and thus it does not cross over to air.

Total internal reflection of light occurs when a light ray is incident in a dense medium above the critical angle.

The critical angle is obtained from Snell's law, and from that we have the formula:

`n=1/sinc`

where `n` is the refractive index of the dense medium and `c` is the critical angle.

`=>c= arsin(1/n)" "` or `" "c=sin^-1(1/(n))`

`=>c=arsin(1/2.42)~=color(blue)(24.4º)`

Thus we see that the values `(i)65.6° (ii)34.4° (iii)74.4°` are all greater than the critical angle,

Hence the light is totally internally reflected.