First slide

Young's double slit Experiment

Question

The ratio of the intensity at the centre of a bright fringe to the intensity at a point one-quarter of the distance between two fringe from the centre is

Moderate

A

2
B

1/2
C

4
D

16

Solution

$I = 4 I_{0} \cos^{2} \frac{ϕ}{2}$
At central position $I_{1} = 4 I_{0}$ …(i)
Since the phase difference between two successive fringes is 2x, the phase difference between two points separated by a distance equal to one quarter of the distance between the two, successive fringes is equal to $δ = (2 π) (\frac{1}{4}) = \frac{π}{2} radian$
$\Rightarrow I_{2} = 4 I_{0} \cos^{2} (\frac{\frac{π}{2}}{2}) = 2 I_{0}$ ….(ii)
Using (i) and (ii) $\frac{I_{1}}{I_{2}} = \frac{4 I_{0}}{2 I_{0}} = 2$

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