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 shwon in Fig. I tis 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

A. `1.21`
B. `1.30`
C. `1.36`
D. `1.42`

Answer

C

Explanation

If `theta` critical angle between the pair of media in contact, then from Fig.

`tan theta = (11.54//2)/(10) = (5.77)/(10) = 0.577`
`:. theta = 30^(@)`
Now `.^(1)mu_(2) = (1)/(sin theta) = (2.72)/(mu) = (1)/(sin 30^(@)) = 2`
`2 mu = 2.72, mu = 1.36`