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Question

What is the speed of light in a medium with a refractive index of 1.5, given the speed of light in
vacuum is \( 3.0 \times 10^8 \, \text{m/s} \)?

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Explanation

**Frequency of light** does not change on refraction, c = f λ, when enters denser medium speed decreases, wavelength decreases λ' = v/f = c/(n f) = λ/n, frequency same, for λ=480 nm f=c/λ=3×10⁸/480×10⁻⁹=6.25×10¹⁴ Hz, for 630 nm f=4.76×10¹⁴ Hz, for 540 nm f=5.56×10¹⁴ Hz, refractive index determines bending. Refractive index n = (c/v) , where c is the speed in vacuum and v is the speed in the medium. Given n = 1.5 , v = (c/n) = (3.0 × 10⁸/1.5) = 2.0 × 10⁸ m/s . Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ, I =

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