Question 238 of 295

A prism of angle $75^{\circ}$ and refractive index $\sqrt{3}$ is coated with thin film of refractive index 1.5 only at the back exit surface. To have total internal reflection at the back exit surface the incident angle must be $\_\_\_\_$
($\sin 15^{\circ}=0.25$ and $\sin 25^{\circ}=0.43$)

A$15^{\circ}$B$\gt 25^{\circ}$Cbetween $15^{\circ}$ and $20^{\circ}$DBoth (1) & (3)

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Answer: (D) Both (1) & (3)

$r_1 + r_2 = 75^{\circ}$
For T I R at back surface
$\sqrt{3} \sin r_2 = \dfrac{3}{2} \sin 90^{\circ}$
$r_2 \geq 60^{\circ}$
$r_1 \leq 15^{\circ}$
$1 \cdot \sin i = \sqrt{3} \sin 15^{\circ}$
$\sin i = 1.73 \times 0.25$
$\sin i = 0.433$
$i = 25^{\circ} \Rightarrow i \lt 25^{\circ}$