Calculate the angle of incidence on the face of a prism of refracting angle `60^(@)` and of refractive index 1.5, for which the emergent ray just grazes the other face.

Explanation

`mu=(sine)/(sinr_(2))`
From figure, `1.5=(sin90^(@))/(sinr_(2))`
`sinr_(2)=1/1.5=0.6667`
`r_(2)=41^(@)49.`
But `r_(1)+r_(2)=A,r_(1)=A-r_(2)=60^(@)-41^(@)49.=18^(@)11.`
`mu=(sini_(1))/(sinr_(1))`
`sini_(1)=musinr_(1)=1.5sin18^(@)11.=1.5xx0.3121=0.4682`
`thereforei_(1)=27^(@)55.`