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?

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 = I_{1}

Intensity of light from slit 2 = I_{2}

Initially let us consider I_{1} = I_{2} = I_{0}

When path difference is λ, the phase difference is 2

Using the formula to find out intensity of resultant wave,

I = I_{1} + I_{2} + 2√(I_{1}I_{2}) cos(θ)

k = I_{0} + I_{0} + 2 cos π = 4I_{0} (∵ Cos(2π) = 1)

k = 4I_{0}

Or, I_{0} = k/4

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

I = I_{1} + I_{2} + 2√(I_{1}I_{2}) cos(θ)

I = I_{0} + I_{0} + 2√(I_{1}I_{2}) cos(2π/3)I_{0} + I_{0} + 2I_{0} × (-1/2) = I_{0} = k/4

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

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