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JEE Main 20178 AprilOnline
Exam
JEE Main
Year
2017
Date
8 April
Mode
Online
Subject
Physics
Chapter
Wave Optics

JEE Main 2017 · 8 April · Online · Physics · Wave Optics

A single slit of width b is illuminated by a coherent monochromatic...

A single slit of width bb is illuminated by a coherent monochromatic light of wavelength λ.\lambda . If the second and fourth minima in the diffraction pattern at a distance 1cm1cm from the slit are at 3cm3cm and 6cm6cm respectively from the central maximum, what is the width of the central maximum? (i.e. distance between first minimum on either side of the central maximum)

Options

  1. A4.5cm4 . 5cm
  2. B1.5cm1 . 5cm
  3. C6.0cm6 . 0cm
  4. D3.0cm3 . 0cm

Correct answer

D. 3.0cm3 . 0cm

Step-by-step solution

For secondary minima dsinθ=nλdsin \theta = n\lambda
sinθ=nλdsin \theta = \dfrac{n\lambda}{d}

For second minima
n=2n = 2
sinθ=2λd=tanθ1=x1Dsin \theta = \dfrac{2\lambda}{d} = tan {\theta}_{1} = \dfrac{{x}_{1}}{D}
For fourth minima n=4n = 4
sinθ2=4λd=x2D{sin \theta}_{2} = \dfrac{4\lambda}{d} = \dfrac{{x}_{2}}{D}

Distance between both minima is x2−x1=4λd−2λd=2λd=6−3=3cm{x}_{2} - {x}_{1} = \dfrac{4\lambda}{d} - \dfrac{2\lambda}{d} = \dfrac{2\lambda}{d} = 6 - 3 =3cm

Width of central maxima,=2λd=3cm= \dfrac{2\lambda}{d} = 3\text{c}\text{m}
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