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JEE Main 201910 JanuaryEvening Shift
Exam
JEE Main
Year
2019
Date
10 January
Shift
Evening Shift
Subject
Physics
Chapter
Wave Optics

JEE Main 2019 · 10 January · Evening Shift · Physics · Wave Optics

Consider a Young's double slit experiment as shown in figure. What...

Consider a Young's double slit experiment as shown in figure. What should be the slit separation dd in terms of wavelength λ\lambda such that the first minima occurs directly in front of the slit (S1)( {S}_{1} ) ?

Consider a Young's double slit experiment as shown in figure. What should be the slit separation d in terms of

Options

  1. A\dfrac{\lambda}{\left(5 - \sqrt{2}\right)}
  2. B\dfrac{\lambda}{2\left(\sqrt{5} - 2\right)}
  3. C\dfrac{\lambda}{2\left(5 - \sqrt{2}\right)}
  4. Dλ5−2\dfrac{\lambda}{\sqrt{5} - 2}

Correct answer

C. \dfrac{\lambda}{2\left(5 - \sqrt{2}\right)}

Step-by-step solution

Consider a Young's double slit experiment as shown in figure. What should be the slit separation d in terms of

Path diff. in front of a slit on screen

∆=5d−2d=(2n−1)λ2∆ = \sqrt{5}d - 2d = \left(2n - 1\right)\dfrac{\lambda}{2}

(for minima)

For 1st{1}^{st} minima n=1n = 1

d(5−2)=λ2d\left(\sqrt{5} - 2\right) = \dfrac{\lambda}{2}

d=λ2(5−2)d = \dfrac{\lambda}{2\left(\sqrt{5} - 2\right)}
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