Question

Two coherent monochromatic light beams of intensities 4I and 9I are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is xI. The value of x is ______.

Hint:

Use the formulas for maximum and minimum intensities in interference. Remember that the intensities are proportional to the square of the amplitudes.

Answer 1

Correct Answer: 24

$I_{max} = (\sqrt{I_1} + \sqrt{I_2})^2$

$I_{max} = (\sqrt{4I} + \sqrt{9I})^2$

$I_{max} = (2\sqrt{I} + 3\sqrt{I})^2$

$I_{max} = (5\sqrt{I})^2 = 25I$

$I_{min} = (\sqrt{I_1} - \sqrt{I_2})^2$

$I_{min} = (\sqrt{4I} - \sqrt{9I})^2$

$I_{min} = (2\sqrt{I} - 3\sqrt{I})^2$

$I_{min} = (-\sqrt{I})^2 = I$

$I_{max} - I_{min} = 24I$

$x = 24$