First slide

Young's double slit Experiment

Question

In Young's double slit experiment the distance between the slits is 1 mm. Find the width of each slit of YDSE setup so that 10th maxima of the double slit pattern is within the central maximum of the single slit pattern?

Moderate

A

0.9 mm
B

0.8 mm
C

0.2 mm
D

0.6 mm

Solution

The angular separation between n
$bright fringes, θ_{n} = \frac{x_{n}}{D} = \frac{n λ}{d}$
$Fringes, θ_{n} = \frac{x_{n}}{D} = \frac{n λ}{d}$
$For 10 bright fringes, θ_{10} = \frac{10 λ}{d}$
The angular width of the central maximum in the diffraction pattern due to slit of width a is
$2 θ_{1} = \frac{2 λ}{a}$
$Now \frac{10 λ}{d} \leq \frac{2 λ}{a} or$
$a \leq \frac{d}{5} = \frac{1}{5} m n = 0.2 mn$

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