First slide

Young's double slit Experiment

Question

In Young's double slit experiment, white light is used. The separation between the slits is b. The screen is at a distance $d (d > b)$ from the slits. Some wavelengths are missing exactly in front of one slit. These wavelengths are

Moderate

A

$λ = \frac{b^{2}}{7 d}$
B

$λ = \frac{2 b^{2}}{d}$
C

$λ = \frac{b^{2}}{3 d}$
D

$λ = \frac{2 b^{2}}{3 d}$

Solution

Path difference between the rays reaching infront of slit S₁ is.
$S_{1} P - S_{2} P = {(b^{2} + d^{2})}^{1 / 2} - d$
For destructive interference at P
$S_{1} P - S_{2} P = \frac{(2 n - 1) λ}{2}$
${(b^{2} + d^{2})}^{1 / 2} - d = \frac{(2 n - 1) λ}{2}$
$\Rightarrow d {(1 + \frac{b^{2}}{d^{2}})}^{1 / 2} - d = \frac{(2 n - 1) λ}{2}$
$\Rightarrow d (1 + \frac{b^{2}}{2 d^{2}} + \dots .) - d = \frac{(2 n - 1) λ}{2}$
(Binomial Expansion)
$\Rightarrow \frac{b}{2 d} = \frac{(2 n - 1) λ}{2} \Rightarrow λ = \frac{b^{2}}{(2 n - 1) d}$
$For n = 1, 2, \dots \dots λ = \frac{b^{2}}{d}, \frac{b^{2}}{3 d}$

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