2008 AIPMT Wave OpticsInterference of Waves Easy Question 36 of 40 in Wave Optics

Two periodic waves of intensities $I_1$ and $I_2$ pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is -

A $(\sqrt{I_1} - \sqrt{I_2})^2$
B $2(I_1 + I_2)$
C $I_1 + I_2$
D $(\sqrt{I_1} + \sqrt{I_2})^2$

The answer is B.

Solution

Resultant intensity for a phase difference $\phi$: $I = I_1 + I_2 + 2\sqrt{I_1 I_2}\cos\phi$
Maximum intensity ($\cos\phi = +1$): $I_{max} = I_1 + I_2 + 2\sqrt{I_1 I_2} = (\sqrt{I_1} + \sqrt{I_2})^2$
Minimum intensity ($\cos\phi = -1$): $I_{min} = I_1 + I_2 - 2\sqrt{I_1 I_2} = (\sqrt{I_1} - \sqrt{I_2})^2$
$I_{max} + I_{min} = (\sqrt{I_1} + \sqrt{I_2})^2 + (\sqrt{I_1} - \sqrt{I_2})^2$
$= (I_1 + I_2 + 2\sqrt{I_1 I_2}) + (I_1 + I_2 - 2\sqrt{I_1 I_2})$
$= 2(I_1 + I_2)$

Concept Maximum and minimum intensity in superposition

Wave Optics in past papers

40 questions from this chapter have appeared across 18 exam years.