Practice question
Question
What is the refractive index of a medium if the speed of light in it is \( 2.5 \times 10^8 \,
\text{m/s} \) and in vacuum is \( 3.0 \times 10^8 \, \text{m/s} \)?
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) . c = 3.0 × 10⁸ m/s , v = 2.5 × 10⁸ m/s . n = (3.0 × 10⁸/2.5 × 10⁸) = 1.2 . Using Δ = d sinθ, y = n λ D/d, a sinθ = n λ, I = I₀ cos²θ, n = c/v, sinC = 1/n, λ'
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