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JEE Main 201911 JanuaryMorning Shift
Exam
JEE Main
Year
2019
Date
11 January
Shift
Morning Shift
Subject
Physics
Chapter
Wave Optics

JEE Main 2019 · 11 January · Morning Shift · Physics · Wave Optics

In a Young's double slit experiment, the path difference, at a...

In a Young's double slit experiment, the path difference, at a certain point on the screen, betwen two interfering waves is 18\frac{1}{8} th of wavelength. The ratio of the intensity at this point to that at the centre of a bright fringe is close to:

Options

  1. A0.74
  2. B0.85
  3. C0.94
  4. D0.8

Correct answer

B. 0.85

Step-by-step solution

Given, path difference, Δx=λ8\Delta x=\frac{\lambda}{8} Phase difference (Δϕ)(\Delta \phi) is given by Δϕ=2πλ(Δx)Δϕ=(2π)λλ8=π4\Delta \phi=\frac{2 \pi}{\lambda}(\Delta \mathrm{x})\Delta \phi=\frac{(2 \pi)}{\lambda} \frac{\lambda}{8}=\frac{\pi}{4} For two sources in different phases, I=I0cos⁡2(π8)1I0=cos⁡2(π8)=1+cos⁡π42=1+122=0.85\begin{array}{l} I=I_{0} \cos ^{2}\left(\frac{\pi}{8}\right)\\ \frac{1}{I_{0}}=\cos ^{2} \left(\frac{\pi}{8}\right)\\ =\frac{1+\cos \frac{\pi}{4}}{2}=\frac{1+\frac{1}{\sqrt{2}}}{2}=0.85 \end{array}
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