In Young's double slit experiment, light from two identical sources are superimposing on a screen. The path difference between the two lights reaching at a point on the screen is 7?/4. The ratio of intensity of fringe at this point with respect to the max

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Solution

Q.
In Young's double slit experiment, light from two identical sources are superimposing on a screen. The path difference between the two lights reaching at a point on the screen is 7λ/4. The ratio of intensity of fringe at this point with respect to the maximum intensity of the fringe is [2024]

1 $\frac{1}{4}$

2 $\frac{1}{3}$

3 $\frac{3}{4}$

4 $\frac{1}{2}$

Ans.
(4)

$Path difference, Δ x = \frac{7 λ}{4}$

$Phase difference, ϕ = \frac{2 π}{λ} Δ x = \frac{2 π}{λ} \times \frac{7 λ}{4} = \frac{7 π}{2}$

$Intensity, I = I_{\max} \cos^{2} (\frac{ϕ}{2})$

$\frac{I}{I_{\max}} = \cos^{2} (\frac{ϕ}{2}) = \cos^{2} (\frac{7 π}{2 \times 2}) = \cos^{2} (\frac{7 π}{4})$

$= \cos^{2} (2 π - \frac{π}{4}) = \cos^{2} \frac{π}{4} = \frac{1}{2}$

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