Question

At what angle should a ray of light be incident on the face of a prism of refracting angle $60^{\circ}$ so that it just suffers total internal reflection at the other face? The refractive index of the material of the prism is $1.524$.

• A. $16^{\circ}$
• B. $29^{\circ}$
• C. $45^{\circ}$
• D. $58^{\circ}$

Answer 1

Answer: (B)

Angle of prism, $A=60^{\circ}$
Refractive index of prism $\mu=1.524$
Let $i$ be the angle of incidence. The critical angle is $i_{C}$ because it just suffers total internal refraction, so we use critical angle.
$\sin i_{c} =\frac{1}{\mu}=\frac{1}{1.524}=0.6561 $
$i_{c} =4 1^{\circ} $
For a prism $r_{1}+r_{2}=A$ here $r_{2}=i_{c}$
$\therefore r_{1}+i_{ c }=A$
$r_{1}+41^{\circ} =60^{\circ} $
$\Rightarrow r_{1} =19^{\circ} $
Using the formula, $\mu=\frac{\sin i_{1}}{\sin r_{1}}$
or $\sin i_{1}=1.524 \sin 19^{\circ}=1.524 \times 0.3256$
Or $i_{1}=\sin ^{-1}(0.4962)$
$i_{1}=29^{\circ} 75'$
Thus, the angle should be $29^{\circ} 75'$.