A parallel beam of monochromatic light is incident on a glass slab at an angle of incidence `60^(@)`. Find the ratio of width of the beam in the glass to that in the air if refractive index of glass is `3//2`.

Explanation

Given `i=60^(@)`, `mu_(g)=(3)/(2)`
Let, `d_(g)=`Width of beam in glass slab,
and `d_(a)=` Width of beam in air
We know that, `._(a)mu_(g)=(sini)/(sinr)`
`(3)/(2)=(sin60^(@))/(sinr)`
`impliessinr=(sqrt(3)xx2)/(2xx3)`
`:.sinr=(1)/(sqrt(3))`
`r=sin^(-1)(0.5773)`
`=35.26^(@)`
`(d_(s))/(d_(a))=(cosr)/(cosi)`
`=(cos35.26^(@))/(cos60^(@))`
`=(0.8164)/(0.5)=1.633`
`(d_(s))/(d_(a))=(16)/(10)=(8)/(5)`
`:.` Ratio of the width of beam `=8 : 5`.