(i) A ray of light incident on face AB of an equilateral glass prism, shows minimum deviation of `30^(@)`. Calculate the speed of the light through the prism.
(ii) Find the angle of incidence at face AB so that the emergent ray grazes along the face AC.

Explanation

(i) For minimum deviation,
As prism is equilatral , `A = 60^(@)`
`sigma = A/2 = (60^(@))/(2) = 30^(@)`
also, `delta_("min") = (mu - 1) 60^(@) = 30^(@)`
`rArr mu = 1/2 + 1 = 3/2`
By Snell's Law,
`(sini)/(sinr) = (mu)/(1) = (v_(1))/(v_(2))`
`mu = c/(sqrt(2)) rArr V_(1) = c/(mu)`
`V_(1) = (3 xx 10^(8))/(3//2)`
`V_(1) = 2 xx 10^(8) ms^(-1)`.
(ii) From Snell's law `(sin i)/(sin r) = mu_(1)^(2)`
Here, Angle of Ref. `90^(@)`
So, `((sini)lambdac)/(sin 90^(@)) = 1/(sqrt(2))`
or, `i = 45^(@)`
`angle` of refraction at AB is `15^(@)`
So, from Snell's law,
`sin_(AB) = sinr_(AB) xx mu_(12) = sin^(-1) (sqrt(2) sin 15^(@))`.