Wave OpticsEasy
Question
Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference between the beams is π/2 at a point A and π at point B. Then the difference between resultant intensities at A and B is
Options
A.2 I
B.4 I
C.5 I
D.7 I
Solution
I(φ) = I1 + 2 + 2
cos φ ......(i)
Here, I1 = I and I2 = 4I
At point A, φ =
∴ IA = I + 4I = 5I
At point B, φ = π ∴ IB = I + 4I - 4I = I
∴ IA - IB = 4I.
Note : Eq. (i) for resultant intensity can be applied only when the source are coherent. In the question it is given that the rays interfere. Interference take place only when the sources are coherent. This is why we applied equation number (i). When the sources are incoherent, the resultant intensity is given by I = I1 + I2.
cos φ ......(i)Here, I1 = I and I2 = 4I
At point A, φ =
∴ IA = I + 4I = 5IAt point B, φ = π ∴ IB = I + 4I - 4I = I
∴ IA - IB = 4I.
Note : Eq. (i) for resultant intensity can be applied only when the source are coherent. In the question it is given that the rays interfere. Interference take place only when the sources are coherent. This is why we applied equation number (i). When the sources are incoherent, the resultant intensity is given by I = I1 + I2.
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