The refractive index of a prism having refracting angle `75^(@)` is `sqrt2` . What should be the minimum angle of incidence on a refracting surface so that the ray will emerge from the other refracting surface of the prism?

Explanation

According to the question, the emergent angle is `i_(2) = 90^(@)`.
So for refraction at the second face of the prism,
`mu = (sini_(2))/(sinr_(2) ) = (sin90^(@))/(sinr_(2))`
`or, " " sinr_(2) = (1)/(mu) = (1)/(sqrt(2)) = sin45^(@) or, r_(2) = 45^(@)`
`"We know", A = r_(1) + r_(2)`
`therefore " " 75^(@) = r_(1) + 45^(@) or, r_(1) = 30^(@)`
For refraction at the first face,
`mu = (sini_(1))/(sinr_(1)) or, sqrt(2) = (sini_(1))/(sin30^(@))`
`or, " " sini_(1) = sqrt(2) xx (1)/(2) = sin45^(@) or, i_(1) = 45^(@)`
`therefore " " "The required angle of incidence" = 45^(@).`