First slide

Young's double slit Experiment

Question

Two coherent sources S₁ and S₂ are separated by a distance four times the wavelength $λ$ of the source. The sources lie along y axis whereas a detector moves along + x axis. Leaving the origin and far off points the number of points where maxima are observed is

Moderate

A

2
B

3
C

4
D

5

Solution

From ${ΔS}_{1} S_{2} D$ ,
${(S_{1} D)}^{2} = {(S_{1} S_{2})}^{2} + {(S_{2} D)}^{2}$
${(S_{1} P + PD)}^{2} = {(S_{1} S_{2})}^{2} + {(S_{2} D)}^{2}$
Here $S_{1} P$ is the path difference $= nλ$ for maximum intensity.
$∴ {(nλ + x_{n})}^{2} = (4 λ)^{2} + {(x_{n})}^{2}$
$or x_{n} = \frac{16 λ^{2} - n^{2} λ^{2}}{2 nλ}$
Then $x_{1} = \frac{16 λ^{2} - λ^{2}}{2 λ} = 7 .5 λ$
$x_{2} = \frac{16 λ^{2} - 4 λ^{2}}{4 λ} = 3 λ$
$x_{3} = \frac{16 λ^{2} - 9 λ^{2}}{6 λ} = \frac{7}{6} λ$
x₄ = 0.
$∴$ Number of points for maxima becomes 3.

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