In a tank filled with a liquid of refractive index `5//3`, a point source of light is placed `2 m` below the surface of water. To cut off all light coming out of water from the source, what should be the minimum diameter of a disc, which should be placed over the source on the surface of water ?

Answer

`3`

Explanation

Here, `mu = 5//3, OC = 2 m, AB = 2 AC = ?`

To cut off all light coming from the source out of water, total internal reflection should occur at `A` and `B`, for which
`mu = (1)/(sin C) = (5)/(3) , sin C = (3)/(5) = sin theta`
`:. tan theta = (4)/(5) = (AC)/(OC), AC = (4)/(5) xx 2 = (8)/(5)m`
`AB = 2 AC = 2 xx (8)/(5)m = (16)/(5)m = 3.2 m`
The correct integral answer is `3 m`