A ray of light is incident at an angle of `60^(@)` on a face of a prism with refracting angle `30^(@)` . If the ray emerges from the other face and makes an angle of `30^(@)` with the incident ray then, show that the emergent ray passes perpendicularly through the refracting surface. Determine the refractive index of the material of the prism.

Explanation

According to question ,`delta = 30^(@), i_(1) = 60^(@) and A = 30^(@)`.
`"We know", delta = i_(1) + i_(2) - A`
`therefore " " 30^(@) = 60^(@) + i_(2) - 30^(@) or, i_(2) = 0`
`therefore` emergent ray is perpendicular to the refracting surface.
`"Again", A = r_(2) + r_(1)`
`"As", i_(2) = 0`, so angle incidence of the second face, `r_(2) = 0`
`therefore " " r_(1) = A = 30^(@)`
`therefore` Refractive index of the material of the prism,
`mu = (sini_(1))/(sinr_(1)) = (sin60^(@))/(sin30^(@)) = ((sqrt(3))/(2))/((1)/(2)) = sqrt(3)`