Given that the angle of the prism is `60^(@)` and its RI for a certain colour 1.645. Calculate the angle of minimum deviation.

Explanation

Given `A=60^(@)" " n =1.645 " " D=`?
`n=(sin((A+D)//2))/(sinA//2)`
`=(sin((60+D)//2))/(sin30)`
`=(sin30^(@)cosD//2+cos30^(@)sinD//2)/(1//2)`
`=(1//2 cos D//2+0.8660 sinD//2)/(1//2)`
`0.8225="sin"(60+D)/(2)`
`(60+D)/(2)=sin^(-1)0.8225`
`(60+D)/(2)=55^(@)20.`
`(60+D)=110^(@)40.`
`D=50^(@)40.`