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The critical angle for a denser-rarer interface is 45°. The speed of light in rarer medium is 3×10⁸ m/s. The speed of light in the denser medium is

Asked in JEE Main 11th April 1st Shift 2023 · Total internal reflection and optical fibres

(1) 5×10⁷ m/s
(2) 2.12×10⁸ m/s
(3) 3.12×10⁷ m/s
(4) √2×10⁸ m/s

Answer: (2) 2.12×10⁸ m/s

Step-by-step solution

sin C=(nᵣ)/(n_d)=(v_d)/(vᵣ).

v_d=vᵣ sin 45°=(3×10⁸)/(√2).

v_d≈2.12×10⁸ m/s.

Why the other options are wrong

(1) Arithmetic slip in the power of ten.
(3) Wrong power of ten and digit in 3 sin 45°.
(4) Writes √2×10⁸ for 3/(√2)×10⁸.

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