(a) If the refracting angle of a prism is `60^@` and the minimum deviation is `30^@`, then find the angle of incidence.
(b) A ray of light passes through an equilateral prism such that the angle of emergence is equal to the angle of incidence and each is equal to `3//4^(th)` of the angle of prism. Find the angle of deviation.
(c) The refracting of a prism is A and the refractive index of the material of the prism is `cotA//2`. Find the angle of deviation.
(d) The angle of a prism is `60^@`. What is the angle of incidence for minimum deviation? The refractive index of the material of the prism is `sqrt2`.

Explanation

(a) `i=(A+delta_m)/(2)=(60+30)/(2)=45^@`
(b) `i=i^'` i.e. `delta=delta_m`
`i=i^'=3/4A=3/4xx60^@=45^@`
`i=(A+delta_m)/(2)implies45=(60+delta_m)/(2)impliesdelta_m=30^@`
(c) `mu=cot(A//2)=(cos(A//2))/(sin(A//2))`
`mu=(sin((A+delta_m)/(2)))/(sin(A/2))`
`(cos(A//2))/(sin(A//2))=(sin((A+delta_m)/(2)))/(sin(A//2))`
`sin(90-A//2)=sin(A/2+delta_m/2)`
`90-A/2=A/2+delta_m/2`
`delta_m/2=90-Aimpliesdelta_m=180^@-2A`
(d) `mu=(sin((A+delta_m)/(2)))/(sin(A//2))`
`sqrt2=(sini)/(sin(60^@//2))=(sini)/(sin30^@)impliesi=45^@`