First slide

Diffraction of light-Wave Optics

Question

In a single slit diffraction of light of wavelength $λ$ by a slit of width e, the size of the central maximum on a screen at a distance b is(Assume the mathematical expression obtained in Fraunhofer diffraction when screen is at $\infty$ distance is also applicable when screen is at finite distance)

Moderate

A

$2 b λ + e$
B

$\frac{2 b λ}{e}$
C

$\frac{2 b λ}{e} + e$
D

$\frac{2 b λ}{e} - e$

Solution

The direction in which the first minima occurs is $θ$ (say).Then $e \sin θ = λ$ or $e θ = λ$ or, $θ = \frac{λ}{e}$ ( $θ = \sin θ$ when $θ$ small)
Width of the central maximum = $2 b θ + e = 2 b . \frac{λ}{e} + e$

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