If the polarizing angle of a piece of glass for green light is `54.74^(@)`, then the angle of minimum deviation for an equilateral prism made of same glass is
[Given : `tan54.74^(@)=1.414`]

Options

A. A)`45^(@)`
B. B)`54.74^(@)`
C. C)`60^(@)`
D. D)`30^(@)`

Answer

D

Explanation

By Brewster.s law, `mu=tantheta_(p)`
or `mu=tan54.74^(@)`
or `mu=1.414`
For an equilateral prism, `angleA=60^(@)`
`therefore mu=(sin""((A+delta_(m))/(2)))/(sin((A)/(2)))`
or `1.414=(sin((60^(@)+delta_(m))/(2)))/(sin((60^(@))/(2)))`
or `(1.414xx1)/(2)=sin((60^(@)+delta_(m))/(2))[because 1.414=sqrt(2)]`
or `(sqrt(2))/(2)=sin((60^(@)+delta_(m))/(2))`
or `(1)/(sqrt(2))=sin((60^(@)+delta_(m))/(2))`
or `45^(@)=((60^(@)+delta_(m))/(2))`
or `delta=30^(@)`