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 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

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

Answer 1

Correct Answer - C
From the given situation , at critical angle , `"tan"theta = ((d//2))/(h) = (5.77)/(10)`

`therefore "sin" theta_(C) = (1)/(2)`
`mu_("denser") "sin"theta_(C) = mu_("rarer") "sin" (pi//2)`
`implies 2.72 xx (1)/(2) = mu_(r) implies mu_(r) = 1.36`