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

Answer 1

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