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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Wave Optics

NTA Abhyas 2020 · Physics · Wave Optics

In a Young's double slit experiment using monochromatic light of...

In a Young's double slit experiment using monochromatic light of wavelengths λ\lambda, the intensity of light at a point on the screen with a path difference λ\lambda is MM units and the intensity of light at a point where the path difference is λ3\dfrac{\lambda}{3} is nMnM units. What is the value of nn?

Correct answer

0.25

Step-by-step solution

Resultant intensity IR=I1+I2+2I1I2cosθ{\text{I}}_{\text{R}} = {\text{I}}_{1} + {\text{I}}_{2} + 2\sqrt{{\text{I}}_{1}{\text{I}}_{2}}cos\theta
If path difference, =λ= \lambda then phase difference =2π….[∵ϕ=2πλ×\Deltax]= 2\pi \ldots . \left[∵ ϕ = \dfrac{2\pi}{\lambda} \times \Deltax\right]
∴IR=I+I+2I×Icos⁡2π…..(∵I1=I2=I)∴ {\text{I}}_{\text{R}} = \text{I} + \text{I} + 2\sqrt{\text{I} \times \text{I}}\cos 2\pi \ldots . . ( ∵ {\text{I}}_{1} = {\text{I}}_{2} = \text{I} )
=4I=M= 4I = M
If path difference =λ3= \dfrac{\lambda}{3}
then phase difference =2πλ×λ3=2π3rad= \dfrac{2\pi}{\lambda} \times \dfrac{\lambda}{3} = \dfrac{2\pi}{3}\text{rad}
IR′=I+I+2I×Icos2π3{I}_{R}^{'} = I + I + 2\sqrt{I \times I}cos\dfrac{2\pi}{3}
=2I+2I(−12)=I=M4=0.25M= 2\text{I} + 2\text{I}\left(\dfrac{- 1}{2}\right) = \text{I} = \dfrac{\text{M}}{4} = 0.25\text{M}
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