A light ray falls on one of the faces of prism at an angle `40^(@)` so that it suffers angle of minimum derivation of `30^(@)` . Find the angle of prism and angle of refraction at the given surface.

Explanation

Incident angle `i=40^(@)`
Angle of minimum deviation, `D=30^(@)`
Let the angle of prism =A
At angle of minimum deviation , `i_(1)=i_(2) and r_(1) = r_(2)`
`therefore A+D=21`
`A+30^(@)=2xx40=80-30=50^(@)`
`therefore `Angle of prism` A=50^(@)`
We know that `A=r_(1) +r_(2)`
At minimum deviation `r_(1)=r_(2)=r`
`therefore A=r+r`
`r=(A)/(2)implies r=(50)/(2) " " therefore r=25^(@)`