A ray of light is incident at an angle of incidents `40^(@)` on a prism having refractive index 1.6 . What should be the value of the angle of the prism for minimum deviation?
Given `sin 40^(@) = 0.6428 , sin 23^(@)42'=0.4018.`

Explanation

`"Here" " " mu = 1.6`.
The angle of incidence at the first face ` = i_(1) = 40^(@)`
Let the angle of emergence at the second face ` = i_(2)` .
For minimum deviation, `i_(1) = i_(2) , "so", i_(2) = 40^(@)`
`therefore " " delta_(m) = i_(1) + i_(2) - A = 40^(@) + 40^(@)-A`
`or, " " A + delta_(m) = 80^(@)`
`"We know", mu = sin""(A + delta)/(2) or, 1.6 = (sin""(80^(@))/(2))/(sin""(A)/(2))`
`or, " " sin""(A)/(2) = (sin 40^(@))/(1.6) = (0.6428)/(1.6)`
`= 0.4018 = sin23^(@)42.`
`therefore " " (A)/(2) = 23^(@)42. or, A = 47^(@)24.`