A ray of light is incident on one face of a transparent glass slab of thickness 9cm at an angle of incidence `60^@`. Lateral displacement of the ray on emerging from the opposite parallel face is `3sqrt3`cm. Refractive index of the material of slab is:

Options

A. `sqrt2`
B. `sqrt3/2`
C. `sqrt(3/2)`
D. `sqrt3`

Answer

D

Explanation

Lateral displacement is given by
`delta=t (sin(i-r))/(cos r)`
`3sqrt3=9(sin (60^@-r))/(cos r)`
`1/sqrt3=(sin 60^@ cos r - cos 60^@ sin r )/ (cos r)`
`1/sqrt3=(sqrt3 cos r - cos 60^@ sin r) /(cos r)`
2 cos r = 3 cos r -`sqrt3 sin r`
`sqrt3` sin r = cos r
`tan r = 1/sqrt3 rArr r=30^@ " " therefore mu=(sin i)/(sin r) =(sin 60^@)/(sin 30^@)=(sqrt3//2)/(1//2)=sqrt3`