A prism of refractive index `1.53` is placed in water of refractive index `1.33`. If the angle of prism is `60^@`, calculate the angle of minimum deviation in water.

Options

A. `4^(@)`
B. `8^(@)`
C. `12^(@)`
D. `16^(@)`

Answer

B

Explanation

Here, `.^(a)mu_(g)=1.5=(3)/(2), .^(a)mu_(w)=1.33=(4)/(3)`
`A=60^(@)`
As `.^(a)mu_(w)xx.^(w)mu_(g)=.^(a)mu_(g)` or `.^(w)mu_(g)=(.^(a)mu_(g))/(.^(a)mu_(w))=((3//2))/((4//3))=(9)/(8)`
`.^(w)mu_(g)=(sin((A+delta_(m))/(2)))/(sin((A)/(2))),(9)/(8)=(sin((60^(@)+delta_(m))/(2)))/sin((60^(@))/(2))`
or `sin((60^(@)+delta_(m))/(2))=(9)/(8)xxsin30^(@)=(9)/(8)xx(1)/(2)=(9)/(16)=0.56`
or `(60^(@)+delta_(m))/(2)=sin^(-1)(0.56)` or `(60^(@)+delta_(m))/(2)=34^(@)`
or `delta_(m)=68^(@)-60^(@)=8^(@)`