The lateral shift for a ray of light incident at `60^(@)` on one face of a rectangular slab of thickness 1 m is 0.577 m. What is the refractive index of the slab.

Explanation

`S _(1) = ( t sin (1 - r ))/( cos r )`
`0.577 = ( sin (60 - r ))/( cos r)`
`implies (1)/( sqrt3) = ( sin (60 - r ))/( cos r )`
`implies r = 30 ^(@)`
`therefore n = ( sin 60 ^(@))/( sin 30 ^(@)) = sqrt3`
`therefore ` Refractive index `= sqrt3`