What will be the angle of emergence of a ray of light through a prism for an angle of incidents `45^(@)` ? The angle of the prism = `60^(@)` , refractive index of the prism =`sqrt2`.

Explanation

`"Hence" " " A = 60^(@) , mu = sqrt(2)`
For refraction at the first face,
`mu = (sini_(1))/(sinr_(1)) or, sqrt(2) = (sin 45^(@))/(sinr_(1))`
`or, " " sinr_(1) = (1)/(sqrt(2)) xx (1)/(sqrt(2)) = (1)/(2) = sin30^(@)`
`or, " " r_(1) = 30^(@)`
`"We know", A = r_(1) + r_(2)`
`therefore " " r_(2) = A - r_(1) = 60^(@) - 30^(@) = 30^(@) = r_(1)`
So, the angle of emergence `(i_(2)) = "angle of incidence" (i_(1)) = 45^(@)`
`therefore` The angle of emergence of the ray of light from the second face is `45^(@)`.