Two coherent point sources S 1 and S 2 vibrating in phase emit light of wavelength λ . The separation between them is 2 λ . The light is collected on a screen placed at a distance D λ from the sli

Question

Two coherent point sources S 1 and S 2 vibrating in phase emit light of wavelength λ . The separation between them is 2 λ . The light is collected on a screen placed at a distance D > > λ from the slit S 1 as shown. The minimum distance, so that intensity at P is equal to the intensity at O

TestHub · Accepted Answer

Path difference between the light waves form $S_{1} a n d S_{2},$ reaching at $P$ is,

$= 2 λ c o s θ$

Since, there is a bright maximum at $O$ . Thus for maximum at $P,$

$2 λ c o s θ = n λ$

For $x$ to be minimum $n = 1$

$c o s θ = \frac{1}{2} \Rightarrow θ = 60 °$

$∴ x = D t a n 60 ° = \sqrt{3} D$

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