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

The incident, refracted, and emerged rays associated with a glass prism ABC are shown in the figure.

Angle of prim, A=`60^(@)`. Refractive index of the prism, `mu=1.524`
`i_(1)` = Incident angle
`r_(1)` = Refracted angle
`r_(2)` = Angle of incidence at the face AC
e=Emergent anlge = `90^(@)` According to Snell's law ,f for face AC, we can have:
`(sine)/(sinr_(2)) = mu`
`sinr_(2)= 1/mu xx sin90^(@)`
`=1/1.524 = 0,6562`
`therefore r_(1) = A-r_(2)= 60-41=19^(@)`
Accoridng to the Snell's law, we have the relation:
`mu=(sini_(1))/(sinr_(1))`
`sini_(1)=musinr_(1)`
`=1.524 xx sin 19^(@)= 0.496`
`therefore i_(1)=29.75^(@)`
Hence, the angle of incidence is `29.75^(@)`.