Question

A point source S is placed at the bottom of a transparent block of height 10 mm and refractive index 2.72. It is immersed in a lower refractive index liquid as shown in the figure. It is found that the light emerging from the block to the liquid forms a circular bright spot of diameter 11.54 mm on the top of the block. The refractive index of the liquid is ______.

Options

• 1.21

• 1.30

• 1.36

• 1.42

Answer 1

The refractive index of the liquid is 1.36.

Explanation:

sin i_c = `r/(sqrt(r^2 + h^2))`

`n_l/n_B = r/(sqrt(r^2 + h^2))`

n_l = `r/(sqrt(r^2 + h^2)) xx n_B`

= `5.77/11.54 xx 2.72  ...[∵ sqrt(r^2 + h^2) = sqrt((5.77)^2 + (10)^2) = 11.54]`

= 1.36