A `60^@` prism has a refractive index of `1.5`. Calculate (a) the angle of incidence for minimum deviation (b) angle of minimum deviation ( c) the angle of emergence of light at maximum deviation (d) angle of maximum deviation.

Explanation

`A=60^@`, `mu=3//2`
(a) `mu=(sin((A+delta_m)/(2)))/(sin(A/2))=(sini)/(sin30^@)`
`3/2=(sini)/(1//2)`
`sini=3/4`
`i=sin^-1(3/4)=49^@`
(b) Maximum deviation will occur, when `i=90^@` i.e. when rays are at grazing incidence.

Refraction at PQ:
`1xxsin90^@=3/2sinrimpliessinr=2/3`
`r=sin^-1(2//3)=42^@`
`r+r^'=A`
`42^@+r^'=60^@impliesr^'=18^@`
Refraction at PR:
`3/2sinr^'=1xxsini^'`
`3/2sin18^@=sini^'`
`3/2xx0.31=sini^'impliessini^'=0.465`
`i^'=sin^-1(0.465)=28^@`