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Two point sources are placed on a straight line separated by distance $d = 10 λ$ where $λ$ is wavelength of the light produced by sources. Both sources having same frequency and are placed at a distance $D (> > d) = 2 m$ from a wall which is perpendicular to straight line as shown in the fig. Both the sources are sending waves of equal intensity. Then which of the following is/are correct

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The locus of point on the wall having equal intensity are circle.

No. of dark rings will be observed on the wall are 10

Radius of 4th bright ring from O is 8/3 m (exclude the position of O)

Radius of 4th bright ring from of is $\sqrt{21} m$ (exclude the position of O)

answer is A, B, C.

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Detailed Solution

$Δ x = S_{1} P - S_{2} P$

$d \cos θ = n λ$ …….. (i)
$Δ x_{\max} = d = 10 λ n λ = 10 λ$
n = 10
From equation (i) for the 4th bright ring
$10 λ \cos θ = 6 λ$

$θ = 53^{0}$

$\cos θ = \frac{3}{5} = \frac{D}{\sqrt{D^{2} + y^{2}}}$
$9 D^{2} + 9 y^{2} = 25 D^{2}$
$y = \frac{8}{3} m$
For dark ring path difference is

$\frac{λ}{2}, \frac{3 λ}{2}, \frac{5 λ}{2}, \frac{7 λ}{2}, \frac{9 λ}{2}, \frac{11 λ}{2}, \frac{13 λ}{2}, \frac{15 λ}{2}, \frac{17 λ}{2}, \frac{19 λ}{2}$

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