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

Explanation

Here, `A=60^(@) and i=(3)/(4) "of" A = (3)/(4) xx 60=45^(@)`.
Using prism formula, we have,
`mu=(sin ((A+deltam)/(2)))/(sin (A)/(2))=(sin i)/(sin A//2) " " [:' i=(A+ delta)/(2)]`
But, `mu=(C)/(V) " " :. (C)/(V)=(sin i)/(sin A//2)`
`rArr (3xx10^(8))/(V)=(sin 45^(@))/(sin 60^(@) //2) rArr (3xx10^(8))/(V)=(sin 45^(@))/(sin 30^(@)) rArr V=(3xx10^(8)xx sin 30^(@))/(sin 45^(@))`
`:. V=(3xx10^(8)xx(1)/(2))/((1)/(sqrt(2)))rArr V=3xx10^(8)=(1)/(2)xxsqrt(2)`
`:. V=1.5xx1.41 xx 10^(8)=2.115xx10^(8)m//s`.