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

`Sin i_(c)=(r)/(sqrt(r^(2)+h^(2)))`
`rArr(n_(l))/(n_(B))=(r)/(sqrt((r^(2))+h^(2)))`
`rArr n_(l)=(r)/(sqrt((r^(2))+h^(2)))xx2.72`
`=(5.77)/(11.54)xx2.72=1.36`