An electromagnetic wave, whose wave normal makes an angle of 45° with the vertical, travelling in air strikes a horizontal liquid surface. While travelling through the liquid it gets deviated through 15°. What is the speed of the electromagnetic wave in the liquid, if the speed of electromagnetic wave in air is 3 × 10⁸ m/s? (sin 30° = 0.5, sin 45° = 1/√(2)) (a) √(2)/3 × 10⁸ m/s (b) 1.5 × 10⁸ m/s (c) 2.1 × 10⁸ m/s (d) 2.5 × 10⁸ m/s

Answer: (c). 45°30°airliquidnormal Angle of incidence (wave normal with the vertical, i.e. the surface normal) i = 45°. Deviation 15° ⇒ angle of refraction r = 45° - 15° = 30°. n = (sin 45°)/(sin 30°) = (1/√(2))/(0.5) = √(2) v = c/n = 3 × 10⁸1.414 ≈ 2.1 × 10⁸ m/s So the answer is (c) 2.1 × 10⁸ m/s.

An electromagnetic wave, whose wave normal makes an angle of 45° with… | MHT CET 2023 (11 May, Shift 2)

Q10MHT CET 2023 · 11 MAY · SHIFT 2Medium

Speed of EM Waves in a Medium

An electromagnetic wave, whose wave normal makes an angle of $45^\circ$ with the vertical, travelling in air strikes a horizontal liquid surface. While travelling through the liquid it gets deviated through $15^\circ$ . What is the speed of the electromagnetic wave in the liquid, if the speed of electromagnetic wave in air is $3 \times 10^{8}\text{ m/s}$ ? $\left(\sin 30^\circ = 0.5, \sin 45^\circ = \frac{1}{\sqrt{2}}\right)$

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Answer: (c)

Angle of incidence (wave normal with the vertical, i.e. the surface normal) $i = 45^\circ$ .
Deviation $15^\circ \Rightarrow$ angle of refraction $r = 45^\circ - 15^\circ = 30^\circ$ .
$n = \dfrac{\sin 45^\circ}{\sin 30^\circ} = \dfrac{1/\sqrt{2}}{0.5} = \sqrt{2}$
$v = \dfrac{c}{n} = \dfrac{3 \times 10^{8}}{1.414} \approx 2.1 \times 10^{8}$ m/s
So the answer is (c) $2.1 \times 10^{8}$ m/s.

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