A point source S is placed at the bottom of a tranparent block of height 10mm 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

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

Answer

C

Explanation

` sin i_(c) = (r)/( sqrt( r^(2) + h^(2)))`
`rArr (1)/( n_(Bi)) = (r)/( sqrt( r^(2) + h^(2)))`

` rArr (n_(l))/( n_(B)) = ((11.54)/(2))/(sqrt(((11.54)/(2))^(2) + 10 ^(2)))`
`rArr n_(1) = (5.77)/( sqrt((5.77)^(2) + (10)^(2))) xx 2 .72 = 1.36`