Light of waveleng

Refractive index in medium 1= n₁ = c/v₁

Refractive index in medium 2 = n₂ = c/v₂

Divide n₁ by n₂

n₁/n₂ = v₂/v₁ …(1)

Wavelength in medium 1 = λ₁

Wavelength in medium 2 = λ₂

Velocity of light in medium 1 = v₁

Velocity of light in medium 2 = v₂

According to the formula,

v = λf where f = frequency

For medium 1: v₁ = λ₁f …(2)

For medium 2: v₂ = λ₂ f ….(3)

divide equation (2) by (3)

v₁/ v₂ = λ₁/λ₂ …(4)

From equation (1) & (4)

v₁/ v₂ = λ₁/λ₂ = n₂/n₁

λ₂ = (n₁/n₂) λ₁