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

Question

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

TestHub · Accepted Answer

The resultant intensity at any point on the screen is given by $I_{R} = I_{1} + I_{2} + 2 I_{1} I_{2} cos ϕ$

At point P, the phase difference is $ϕ_{P} = \frac{π}{2}$

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

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

At point Q, the phase difference is $ϕ_{Q} = π$

$I_{Q} = I + 9 I + 2 I (9 I) cos (π)$

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

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

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

Answer: $6 I$

Physics - Wave Optics Question with Solution | TestHub

Options:

Doubts & Discussion