By making an appropriate substitution, write a mathematical expression for λ2, in terms of ν1, ν2 and λ1. Show all your work.

Question

The relationship between the velocity (ν), frequency (f), and wavelength (λ) of a wave is given by: ν = fλ. Since the frequency remains constant when light travels between different media, an expression can be written to solve for λ2. For medium 1, ν1 = fλ1 and for medium 2, ν2 = fλ2. By making an appropriate substitution, write a mathematical expression for λ2, in terms of ν1, ν2 and λ1. Show all your work.

Answer 1

V₁ = fλ₁ and V₂ = fλ₂

f = V₂ / λ₂

Substitute the last expression for f into V₁ = fλ₁ to get V₁ = V₂ / λ₂ x λ₁.

Solving for λ₂ = V₂ / V₁ x λ₁

_{I hope this helps.}