Question

A parallel sides slab ABCD of refractive index 2 is sandwiched between two slabs of refractive indices $\sqrt{2}$ and $\sqrt{3}$ as shown in the figure. The minimum value of angle such that the ray PQ suffers total internal reflection at both the surfaces AB and CD

• A. ${30}^o$
• B. ${45}^o$
• C. ${60}^o$
• D. ${75}^o$

Answer 1

Answer: (C)

${60}^o$

Critical angle for total internal reflection,The angle of incidence should be greater than equal to ${\theta }_c={\sin }^{-1}\left(\frac{n_2}{n_1}\right)$

For surface AB,

${\theta }_{C1}={\sin }^{-1}\left(\frac{\sqrt{2}}{2}\right)={45}^{\circ }$

For surface DC,

${\theta }_{C2}={\sin }^{-1}\left(\frac{\sqrt{3}}{2}\right)={60}^{\circ }$

For total internal reflection at both surfaces angle of incidence should be greater than equal to both ${45}^{\circ }$ and ${60}^{\circ }$.

So angle of incidence is ${60}^{\circ }$