In Young’s double-slit experiment using monochromatic light of wavelength λ, the intensity of light at a point on the screen where path difference is λ, is K units. What is the intensity of light at a point where path difference is λ/3?

Question

Philoid · Accepted Answer

Given:

Wavelength of monochromatic light = λ

Intensity of light at a point on the screen where path difference is λ = K units.

Intensity of light at any point = I

Intensity of light from slit 1 = I₁

Intensity of light from slit 2 = I₂

Initially let us consider I₁ = I₂ = I₀

When path difference is λ, the phase difference is 2

Using the formula to find out intensity of resultant wave,

I = I₁ + I₂ + 2√(I₁I₂) cos(θ)

k = I₀ + I₀ + 2 cos π = 4I₀ (∵ Cos(2π) = 1)

k = 4I₀

Or, I₀ = k/4

When path difference is λ/3, the phase difference is 2/3

I = I₁ + I₂ + 2√(I₁I₂) cos(θ)

I = I₀ + I₀ + 2√(I₁I₂) cos(2π/3)I₀ + I₀ + 2I₀ × (-1/2) = I₀ = k/4

Intensity of light when path difference is λ/3 is k/4.