A prism of angle 75 ° and refractive index 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 = 0 . 25 and sin 2

Question

A prism of angle $75 °$ 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 ______.

$(\sin 15 ° = 0.25 and \sin 25 ° = 0.43)$ [2026]

Smart Achievers · Accepted Answer

(4)

$\sqrt{3} $

$For TIR at back surface$

$\sqrt{3} \sin r_{2} = \frac{3}{2} \sin 90 °$

$r_{2} > 60 °$

$r_{1} < 15 °$

$\sin i = \sqrt{3} \sin 15 °$

$\sin i = 1.73 \times 0.25$

$\sin i = 0.433$

$i = 25 ° \Rightarrow i < 25 °$

Solution

Q.
A prism of angle $75 °$ 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 ______.

$(\sin 15 ° = 0.25 and \sin 25 ° = 0.43)$ [2026]

1 $15 °$

2 between $15 ° a n d 20 °$

3 $< 15 °$

4 None of these

Ans.
(4)

$r_{1} + r_{2} = 75 °$

$For TIR at back surface$

$\sqrt{3} \sin r_{2} = \frac{3}{2} \sin 90 °$

$r_{2} > 60 °$

$r_{1} < 15 °$

$\sin i = \sqrt{3} \sin 15 °$

$\sin i = 1.73 \times 0.25$

$\sin i = 0.433$

$i = 25 ° \Rightarrow i < 25 °$

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Solution

Q. A prism of angle 75° and refractive index 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 ______. (sin15°=0.25 and sin25°=0.43) [2026]

1 15°

2 between 15° and 20°

3 <15°