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14.10 Interference

14.10.1 Superposition of Two Waves of Same Frequency but Constant Phase Difference

Resultant intensity I which is proportional to the square of the resultant amplitude, is given as





(Here we have taken the constant of proportionality as 1, for simplicity).

The intensity I is maximum when cos d = + 1, that is, when phase difference is given by

d = 2n p (even multiple of p).

From Eq.

The intensity I is minimum when cos d = –1, i.e., when d is given by

(odd multiple of p).

We have from eq.



The resultant intensity is thus less than the sum of two separate intensities. If I1 = I2 then Imin= 0, which means that there is no light.

In general, for the two waves of same intensity and having a constant phase difference of d, the resultant intensity is given by

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