First slide

Young's double slit Experiment

Question

The path difference between two interfering waves of equal intensities at a point on the screen is $λ / 4$ . The ratio of intensity at this point and that at the central fringe will be

Moderate

A

1 : 1
B

1 : 2
C

2 : 1
D

1 : 4

Solution

By using $I = 4 I_{0} \cos^{2} (\frac{ϕ}{2}) = 4 I_{0} \cos^{2} (\frac{πΔ}{λ})$
$\{∵ ϕ = \frac{2 π}{λ} Δ\}$
$\Rightarrow \frac{I_{1}}{I_{2}} = \frac{\cos^{2} (\frac{{πΔ}_{1}}{λ})}{\cos^{2} (\frac{{πΔ}_{2}}{λ})} = \frac{\cos^{2} (\frac{π \cdot \frac{λ}{4}}{λ})}{\cos^{2} (0)} = \frac{1}{2}$

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