Egor asked in Science & MathematicsPhysics · 1 year ago

How o I find the index of refraction using only wavelength? (2.2 m in deep water and 1.6 m in shallow water)?

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  • 1 year ago

    Moving from deep water to shallow water, refractive index = 2.2/1.6 = 1.375

    (You might be expected to round to 1.38 or 1.4)

    Explanation:

    When the wave moves from one medium to another, the frequency stays the same.  (If it didn't, there would be a discontinuity at the boundary with the water on the 2 sides moving up/down at different frequencies -  which isn't physically possible.)

    In medium 1: v₁ = λ₁f

    In medium 2: v₂ = λ₂f

    v₁/v₂ = λ₁/λ₂

    The refractive index going from medium 1 to medium 2 is ₁n₂ = v₁/v₂ = λ₁/λ₂

    The refractive index going from medium 2 to medium 1 is ₂n₁ = v₂/v₁ = λ₂/λ₁

    Going from deep water to shallow water, refractive index = 2.2/1.6 = 1.375

    or

    Going from shallow water to deep water, refractive index =1.6/2.2 = 0.727

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