At what angle should a ray of light be incident on the face of a prism of refracting angle `60^(@)` so that it just suffers total internal reflection at the other face ? The refractive index of the prism is 1.524.

Explanation

Given, refractive index, `mu = 1.524`
Let a ray of light be incident on one face PQ of the prism at an angle of incidence i. It will undergo total internal reflection at the other face when the refracted ray is incident at the critical angle.

Critical angle is given by
`sin i_(c )=(1)/(mu)=(1)/(1.524)`
`sin i_(c )=0.6561=sin 41^(@)`
`therefore" "i_(c )=41^(@)`
For TIR at other face, `r.=i_(c )=41^(@)`
Also, for a prism
`A=r+r.`
`r=A-r.`
`=60^(@)-41^(@)=19^(@)`
Using Snell.s law,
`(sini)/(sinr)=1.524`
`rArr" "sini=sin19^(@)xx1.524`
`therefore" "i=29.7^(@)~~30^(@)`