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Four coherent and monochromatic sources of light, emit light of wavelength $λ$ travelling along x axis and each having intensity $l_{0},$ are placed along x-axis at $x = 0, d, 2 d$ and $3 d$ . Let P be a far away point on the x-axis. Then at point P

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There will be minima if $d= \frac{λ}{4}$

Intensity is ${4l}_{0}$ if $d= \frac{λ}{2}$

Intensity is ${3l}_{0}$ if $d = \frac{λ}{6}$

There will be minima if $d= \frac{λ}{8}$

answer is A, D.

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Detailed Solution

When $d = \frac{λ}{4} =$ path difference

Phase difference $= \frac{2 π}{λ} (\frac{λ}{4}) = \frac{π}{2}$

Intensity

When $d = \frac{λ}{6}, Δ ϕ = \frac{2 π}{λ} (\frac{π}{6}) = \frac{π}{3}$

$A_{n e t} = 2 A_{0} \cos 30 °$

$A_{n e t} = \frac{\sqrt{3}}{2} A \times 2 = \sqrt{3} A_{0}$

$l_{n e t} = 3 l_{0}$

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