Question

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.

Answer 1

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

The angle of the prism, A=60º
The refractive index of the prism, μ= 1.524
i1= Incident angle
r1= Refracted angle
r2= Angle of the incident at the face AC e= Emergent angle= 90º
According to Snell's law, for face AC, we can have $\frac{sin_e}{sin\,r_2}$= μ
sinr2= $\frac{1}{\mu}$ × sin90º= $\frac{1}{1.524}$= 0.6562
∴r2= sin-1 0.6562 ≈ 41°
∴r1= A - r2= 60 - 41= 19°
It is clear from the figure that angle A= r1 + r2
According to Snell's law, we have the relation: $\mu=\frac{sin\,i_1}{sin\,r_1}$
$sin\,i_1=\mu sin\,r_1$= 1.524 × sin19º= 0.496
∴i1 = 29.75º
Hence, the angle of incidence is 29.75º.