Question:

Two sources of light of wavelength $2500\, ? $ and $3500 \,? $ are used in Young?? double slit experiment simultaneously. Which orders of fringes of two wavelength patterns coincide?

Updated On: Jul 7, 2022

$3^{rd}$ order of $1^{st}$ source and $5^{th}$ of the $2^{nd}$
$7^{th}$ order of $1^{st}$ and $5^{th}$ order of $2^{nd}$
$5^{th}$ order of $1^{st}$ and $3^{rd}$ order of $2^{nd}$
$5^{th}$ order of $1^{st}$ and $7^{th}$ order of $2^{nd}$

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The Correct Option is B

Solution and Explanation

Let $n^{th}$ fringe of $2500 ?$ coincide with $\left(n - 2 \right) ^{th}$ fringe of $3500 ?$. $\therefore 3500\left(n-2\right) = 2500 \times n $ $ 1000 n = 7000$, or $ n = 7 $ $ \therefore 7^{th}$ order fringe of $1^{st }$ source will coincide with $5^{th}$ order fringe of $2^{nd}$ source,

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Concepts Used:

Young’s Double Slit Experiment

Considering two waves interfering at point P, having different distances. Consider a monochromatic light source ‘S’ kept at a relevant distance from two slits namely S₁ and S₂. S is at equal distance from S₁ and S₂. SO, we can assume that S₁ and S₂ are two coherent sources derived from S.
The light passes through these slits and falls on the screen that is kept at the distance D from both the slits S₁ and S₂. It is considered that d is the separation between both the slits. The S₁ is opened, S₂ is closed and the screen opposite to the S₁ is closed, but the screen opposite to S₂ is illuminating.
Thus, an interference pattern takes place when both the slits S₁ and S₂ are open. When the slit separation ‘d ‘and the screen distance D are kept unchanged, to reach point P the light waves from slits S₁ and S₂ must travel at different distances. It implies that there is a path difference in the Young double-slit experiment between the two slits S₁ and S₂.