Two coherent beams of wavelength 5000 A ∘ reaching a point would individually produce intensities 1.44 and 4.00 units. If they reach there together, the intensity is 10.24 units. Calculate the lowest

Question

Two coherent beams of wavelength 5000 A ∘ reaching a point would individually produce intensities 1.44 and 4.00 units. If they reach there together, the intensity is 10.24 units. Calculate the lowest phase difference with which the beams reach that point.

TestHub · Accepted Answer

Resultant intensity at the point where the two coherent beam reach together is given by

$I = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2}} \cos ϕ$

$\Rightarrow 10.24 = 1.44 + 4.00 + 2 \sqrt{1.44 \times 4.00} \cos ϕ$

$\Rightarrow 10.24 = 5.44 + 4.8 \cos ϕ$

$\Rightarrow \cos ϕ = \frac{10.24 - 5.44}{4.8} = 1$

$\Rightarrow ϕ = 0$

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