A ray of monochromatic light suffers minimum deviation of `38^(@)` while passing through a prism of refracting angle `60^(@)` . Refracting index of the prism material is

Answer

3

Explanation

`S=i_(1)+i_(2)-A`
`i_(1)+i_(2)=90^(@)`
`i_(1)-i_(2)=30^(@)`
`i_(1)=60^(@)`
`i_(2)=30^(@)`
`r_(1)+r_(2)=60^(@)`
`r_(1)=60-r_(2)`
`sini_(1)=musinr_(1)`
`sini_(2)=musinr_(2)`
`sin60^(@)=musin(60-r_(2))`
`(sqrt(3))/(2)=mu`
`mu[(sqrt(3))/(2)1-sin^(2)r_(2)-(1)/(2)(sini_(2))/(mu)]`
gives `4mu^(2)-1=[(1+2sqrt(3))/(sqrt(3))]^(2)`