Ncert Exercises & Solutions

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

Hint: \(I=I_{1}+I_{2}+2 \sqrt{I_{1} I_{2}} \cos \phi\)
Step 1: Find phase difference.
\(\Delta \phi=\frac{2 \pi}{h} \times \Delta x=\frac{2 \pi}{\lambda} \times \lambda =2 \pi\)
Step 2: Find the resultant intensity
\(\begin{aligned} I &=I_ 0+I_ 0+2 \sqrt{I_{0}} I_{0} \cos \phi \\ &=2 I_{0}(1+\cos \phi) \\ &=\operatorname{} 4 I_{0} \cos ^{2} {\phi \over 2 }\\ &= 4 \operatorname{I}_{0}=K \end{aligned}\)
Step3: Find the new intensity of light

\(I' = 4I_0~cos^2 ({2 \pi /3 \over 2}) = 4I_0 cos^2 ({ \pi \over 3})\\ \\ = 4I_0 \times {1 \over 4}\\ \\ \\ = {K \over 4}\)

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