An isosceles glass prism has one of its faces silvered. A light ray is incident normally on the other face which is identical in size to the silvered face. The light ray is reflected twice on the same sized faces and emerges through the base of the prism perpendicularly. Find the minimum value of refractive index of the material of the prism.

Explanation

Given, `r_(1)=0`
`therefore r_(2)=A=180^(@)-2theta`

`angleDFE=180^(@)-90^(@)-2r_(2)`
`=180^(@)-90^(@)-360^(@)+4theta`
`=4theta-270^(@)`…(ii)
`therefore r_(3)=90^(@)-angleDFE=360^(@)-4theta....(iii)`
`angleBFG=90^(@)-theta=90^(@)-r_(3)`
or `r_(3)=theta`....(iv)
From Eqs. (iii) and (iv), we have
`5 theta=360^(@)`
`therefore theta=72^(@) and 180^(@)-2theta=36^(@)`
`therefore` Angles of prism are `72^(@),72^(@) and 36^(@)`