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 'T' units. What is the intensity of light at a point where path difference is $\frac{λ}{4}$?

$\frac{T}{2}$

The correct answer is Option (4) → $\frac{T}{2}$

In young double slit experiment the intensity at a point on the screen is -

$I=I_0(1+\cos \phi)$

where,

$I_0$, Maximum intensity (constructive interference)

$\phi$, Phase difference between the waves.

$\phi=\frac{2πΔx}{λ}$

Case 1: Path difference = $λ$

$\phi=\frac{2πλ}{λ}=2π$

$∴T=I_0(1+\cos 2π)$

$=2I_0$

Case 2: 

Path difference = $λ/4$

$Δx=λ/4$, the phase difference

$\phi=\frac{2π(λ/4)}{λ}=\frac{π}{2}$

At $\phi=\frac{π}{2},\cos \phi=0$

$I=I_0(1+\cos\frac{π}{2})=I_0$

$∴I=\frac{T}{2}$