A ray of light is incident normally on one face of `30^(@) - 60^(@) - 90^(@)` prism of refractive index 5/3 immersed in water of refractive index 4/3 as shown in figure .

Options

A. The exit angle of `theta_(2)` of the ray is `sin^(-1)(5//8)`
B. The exit angle `theta_(2)` of the ray is `sin^(-1)((5)/(4sqrt(3)))`
C. Total internal reflection at point P ceases if the refractive index of water is increased to `(5)/(2sqrt(3))` by some substance
D. Total internal reflection at point P ceases if the refractive index of water is increased to 5/6 by dissolving some substance

Answer

A,C

Explanation

`theta_(1) = 60^(@)`
`(5)/(3)"sin"30^(@)= (4)/(3)"sin"theta_(2)`
`"sin"theta_(2)= (5)/(8)`
`theta_(2) = sin^(-1)(5)/(8)`
Also (C), TIR is at P ceases if
`(5)/(3) "sin"60^(@) = muxx "sin"90^(@), (5 xx sqrt(3))/(3 xx2) = mu`