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Question

The angular width of the central maximum in a single slit diffraction pattern is 60. The width of the slit is 1 μm. The slit is illuminated by monochromatic plane waves. If another slit of the same width is made near it, Young's Fringes can be observed on a screen placed at a distance 50 cm from the slits. If the observed fringe width is 1 cm. What is slit separation distance? (i.e. distance between the centre of each slit)

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Solution



In single slit diffraction,

The angular width of central maximum is given by 2θ

Where, θangular position of first minimum

Given that, 2θ=60
θ=30

The condition or first minimum is given by,

asinθ=λ

1×106sin30=λ

λ=0.5×106m=5×107m



In YDSE,

Fringe width, β=λDd

Where d = distance between the slits

1×102=5×107×50×102d

d=25×106 m=25 μm

Why this question?Asked in JEE mains 2018.

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