When a glass prism of refracting angle `60^@` is immersed in a liquid its angle of minimum deviation is `30^@`. The critical angle of glass with respect to the liquid medium is

Options

A. `42^@`
B. `45^@`
C. `50^@`
D. `52^@`

Answer

B

Explanation

Refractive index of prism with respect to liquid is given as,
`mu = sin((A+D_(m))/2)/(sin(A/2)) = sin((60^@+30^@)/2)/(sin(60/2))`
` therefore mu=(sin45^@)/(sin30^@)=(1/sqrt(2))/(1/2) =sqrt(2)`
`therefore “critical angle”= sin^(-1)(1/mu)=sin^(-1)(1/sqrt(2))=sin^(-1)(sin45^@)=45^@`