Q21 of 26 Page 1

Two harmonic waves of monochromatic light

are superimposed on each other. Show that maximum intensity in interference pattern is four times the intensity due to each slit. Hence write the conditions for constructive and destructive interference in terms of the phase angle φ.

Here, we use the principle of superposition. The resultant displacement is given by



Hence, the amplitude of displacement is .


Now, the intensity is directly proportional to the square of the amplitude.


Hence,


Where I0=a2 is the intensity of each harmonic wave.


In the case of constructive interference, we have maximum intensity.


This will happen when cosine of the angle is highest.


Thus,




And for destructive interference, cosine of the angle is minimum.


Hence,



ANS


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