Two coherent point light sources are placed at $x = - d / 2 and x = d / 2$ . These sources are surrounded by a spherical screen having equation $x^{2} + y^{2} + z^{2} = R^{2} (R >> d)$ . The sources emit monochromatic light of wavelength = d/3

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The shape of second order maxima is a circle of radius. $\frac{2 R \sqrt{5}}{3}$

The number of maxima produced on the screen are 7

All maxima are equally spaced along x-axis

If radius of screen is doubled the intensity of maxima will become one fourth

answer is A, C, D.

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Detailed Solution

Order of maxima are 3, 2, 1, 0 ,1 ,2, 3
Along x-axis: $(\frac{d}{2} + π) - (\frac{d}{2} - π) == n λ$
$\begin{array}{l} 2 π = n λ \\ π_{1} = \frac{λ}{2} x_{2} = \frac{2 λ}{2} x_{3} = \frac{3 λ}{3} \end{array}$
Hence $π_{2} - π_{1} = π_{3} - π_{2}$ also
$\begin{aligned} dcos θ = n λ \\ 3 λ \cos θ = 2 λ \\ \cos θ = \frac{2}{3} \\ \sin θ = \frac{\sqrt{5}}{3} \end{aligned}$
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$\begin{aligned} r = R \sin θ \\ r = \frac{R \sqrt{5}}{3} \end{aligned}$