Interference fringes are produced on the screen by using two light sources of intensities I and 9I. The phase difference between the beams is π /2 at point P and π at point Q on the screen. The differ

Question

Interference fringes are produced on the screen by using two light sources of intensities I and 9I. The phase difference between the beams is π /2 at point P and π at point Q on the screen. The difference between the resultant intensities at points P and Q is ( cos 9 0 ∘ = 0 , cos π = − 1 )

TestHub · Accepted Answer

The resultant intensity in interference is given by $I_{R} = I_{1} + I_{2} + 2 I_{1} I_{2} cos ϕ$ .

Given $I_{1} = I$ and $I_{2} = 9 I$ .

At point $P$ , the phase difference is $ϕ = π /2$ .

$I_{P} = I + 9 I + 2 I \times 9 I cos (π /2)$

$I_{P} = 10 I + 0 = 10 I$

At point $Q$ , the phase difference is $ϕ = π$ .

$I_{Q} = I + 9 I + 2 I \times 9 I cos π$

$I_{Q} = 10 I + 2 (3 I) (- 1) = 10 I - 6 I = 4 I$

The difference between the resultant intensities at points $P$ and $Q$ is:

$I_{P} - I_{Q} = 10 I - 4 I = 6 I$

Answer: 6 I

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