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 $\frac{λ}{4}$?
Answer & explanation
Correct answer: option 4
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 $\phi=\frac{π}{2},\cos \phi=0$
$I=I_0(1+\cos\frac{π}{2})=I_0$
$∴I=\frac{T}{2}$