First slide

Coherent sources and their importance in interference

Question

The maximum intensity in Young's double slit experiment is I₀. Distance between the slits is d = 5 $λ$ , where $λ$ is the wavelength of monochromatic light used in the experiment. The intensity of light in front of one of the slits on a screen at a distance D = 10d is

Moderate

A

$\frac{I_{0}}{2}$
B

$\frac{3}{4} I_{0}$
C

$I_{0}$
D

$\frac{I_{0}}{4}$

Solution

Suppose P is a point in front of one slit at which intensity is I₀. From figure, it is clear that $y = \frac{d}{2}$ . Path difference between the waves reaching at P is
$Δx = \frac{yd}{D} = \frac{(\frac{d}{2}) d}{10 d} = \frac{d}{20} = \frac{5 λ}{20} = \frac{λ}{4}$

Hence corresponding phase difference is given by
$ϕ = \frac{2 π}{λ} \times \frac{λ}{4} = \frac{π}{2}$
Resultant intensity at P is
$I = I_{max} \cos^{2} (\frac{ϕ}{2}) = I_{0} \cos^{2} (\frac{π}{4}) = \frac{I_{0}}{2}$

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