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 material of the prism is 1.524.
The incident, refracted, and emergent rays associated with a glass prism ABC are shown in the given figure.
Angle of prism, ∠A = 60°
Refractive index of the prism, µ = 1.524
`i_1` = Incident angle
`r_1` = Refracted angle
`r_2` = Angle of incidence at the face AC
e = Emergent angle = 90°
According to Snell’s law, for face AC, we can have:
`(sin e)/(sin r_2) = mu`
`sin r_2 = 1/mu xx sin 90^@`
`= 1/1.524 = 0.6562`
`:. r_2 = sin^(-1) 0.6562 ~~ 41^@`
It is clear from the figure that angle `A = r_1 + r_2`
`:. r_1 = A - r_2 = 60 - 41 = 19^@`
According to Snell’s law, we have the relation:
`mu = (sin i_1)/(sin r_1)`
`sin i_1 = mu sin r_1`
`= 1.524 xx sin 19^@ = 0.496`
`:. i_1 = 29.75^@`
Hence, the angle of incidence is 29.75°.