Physics · Geometrical Optics

NEET (UG) 2023 — Question 17

Light travels a distance $x$ in time $t_{1}$ in air and $10 x$ in time $t_{2}$ in another denser medium. What is the critical angle for this medium?

Option A:
$\sin ^{-1}\left(\frac{10 t_{2}}{t_{1}}\right)$
Option B:
$\sin ^{-1}\left(\frac{t_{1}}{10 t_{2}}\right)$
Option C:
$\sin ^{-1}\left(\frac{10 t_{1}}{t_{2}}\right)$
Correct
Option D:
$\sin ^{-1}\left(\frac{t_{2}}{t_{1}}\right)$

Answer: C

Step-by-step solution

For critical angle, Snell's law: $\mu_2 \sin i_c = \mu_1 \sin 90^\circ = \mu_1$ . So $\sin i_c = \frac{\mu_1}{\mu_2}$ . Refractive index $\mu = \frac{c}{v}$ . Thus $\sin i_c = \frac{c/v_1}{c/v_2} = \frac{v_2}{v_1}$ . Speed in air: $v_1 = \frac{x}{t_1}$ . Speed in denser medium: $v_2 = \frac{10x}{t_2}$ . Substitute: $\sin i_c = \frac{10x/t_2}{x/t_1} = \frac{10 t_1}{t_2}$ . Therefore, critical angle $i_c = \sin^{-1}\left(\frac{10 t_1}{t_2}\right)$ . That matches option C.

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Exam: NEET (UG) 2023
Paper: 2023 paper
Subject: Physics
Chapter: Geometrical Optics
Topic: Introduction to Refraction of Light (Snell's Law)

Answer: C

Step-by-step solution

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