1. sin⁻¹(10t₁/t₂) 2. sin⁻¹(t₂/t₁) 3. sin⁻¹(10t₂/t₁) 4. sin⁻¹(t₁/10t₂)

Answer: 1. sin⁻¹(10t₁/t₂) Refractive index n=c/v , and the critical angle satisfies sin C=1/n=v/c . Speed in air: c=x/t₁ . Speed in the medium: v=10x/t₂ . sin C=v/c=10x/t₂/x/t₁=10t₁/t₂ . So C=sin⁻¹(10t₁/t₂) , option 1.

Topic: Total internal reflection and applications· Optics

Light travels a distance x in time t_1 in air and 10x in time t_2 in another denser medium. What is the critical angle for this medium?

1. \(\sin^{-1}\left(\frac{10t_1}{t_2}\right)\)

2. \(\sin^{-1}\left(\frac{t_2}{t_1}\right)\)

3. \(\sin^{-1}\left(\frac{10t_2}{t_1}\right)\)

4. \(\sin^{-1}\left(\frac{t_1}{10t_2}\right)\)

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Answer: 1. \(\sin^{-1}\left(\frac{10t_1}{t_2}\right)\)

Refractive index \(n=\dfrac{c}{v}\), and the critical angle satisfies \(\sin C=\dfrac1n=\dfrac vc\).

Speed in air: \(c=\dfrac{x}{t_1}\).
Speed in the medium: \(v=\dfrac{10x}{t_2}\).
\(\sin C=\dfrac{v}{c}=\dfrac{10x/t_2}{x/t_1}=\dfrac{10t_1}{t_2}\).

So \(C=\sin^{-1}\!\left(\dfrac{10t_1}{t_2}\right)\), option 1.

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report

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Light travels a distance x in time t_1 in air and 10x in time t_2 in another denser medium. What is the critical angle for this medium?

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