A ray of light passing through an equilateral traingular glass prism from air undergoes minimum deviation when angle of incidence is `3//4` th of the angle of prism. Calculate the speed of light in the prism.

Options

A. `2.5 xx 10^(8)` m/s
B. `1.75 xx 10^(8)` m/s
C. `2.12 xx 10^(8)` m/s
D. `2 xx 10^(8)` m/s

Answer

C

Explanation

`i= (3)/(4) A = (3)/(4) xx 60^(@) = 45^(@)`
When it suffers minimum deviation `r = (A)/(2) = 30^(@)`
`therefore n = (sin i)/(sin r) = (sin 45^(@))/(sin 30^(@)) = (1 // sqrt2)/(1//2) = sqrt2 = 1.414`
`therefore` Velocity of light in glass `= (C)/(n) = ( 3 xx 10^(10))/(1.414)`
`therefore V = 2.12 xx 10^(8)` m/s