Question

White light is incident on a soap film of refractive index
at an angle of refraction 30° The reflected light
is observed to have a dark band for wavelength 6 x 10-5 cm. Calculate the minimum thickness of the film.

Answer 1

The refractive index, μ = 4/3 = 1.33 is also given in the question.

Given:

Angle of refraction, r = 30°

Wavelength, λ = 6 x 10⁻⁵ cm = 6 × 10⁻⁷ m

Refractive index, μ = 4/3 = 1.33

To Find:

The minimum thickness of the film.

Calculation:

- For dark band, there should be destructive interference.

- Path difference = Δx = (n+ 1/2)λ

- For minimum thickness, n=0

⇒ 2μt cosr = λ/2 ⟹ t = λ/4μ cosr

⇒ t = 6 × 10⁻⁷/ 4 × 1.33 × cos 30

⇒ t = 6 × 10⁻⁷/ 5.32 × 0.5

⇒ t = 2.256 × 10⁻⁷ m

- So the thickness of the film is 2.256 × 10⁻⁷ m.