First slide

Coherent sources and their importance in interference

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

Difficult

A

$λ = \frac{b^{2}}{d}$
B

$λ = \frac{2 b^{2}}{d}$
C

$λ = \frac{4 b^{2}}{3 d}$
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 distructive interference at P
$S_{1} P - S_{2} P = \frac{(2 n - 1) λ}{2}$
i.e $(b^{2} + d^{2})^{1 / 2} - d = \frac{(2 n - 1) λ}{2}$
$\Rightarrow d {(1 + \frac{b^{2}}{d^{2}})}^{1 / 2} - d = \frac{(2 n - 1) λ}{2}$
$\Rightarrow d (1 + \frac{b^{2}}{2 d^{2}} + . . . . . .) - d = \frac{(2 n - 1) λ}{2}$
(Binomial Expansion)
$\Rightarrow \frac{b}{2 d} = \frac{(2 n - 1) λ}{2} \Rightarrow λ = \frac{b^{2}}{(2 n - 1) d}$
For $n = 1, 2 . . . . . . . . . . . ., λ = \frac{b^{2}}{d}, \frac{b^{2}}{3 d}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App