Question

Two waves of intensity ratio $1 : 9$ cross each other at a point. The resultant intensities at the point, when (a) Waves are incoherent is $I_1$ (b) Waves are coherent is $I_2$ and differ in phase by $60^\circ$ If $\frac{I_1}{I_2} = \frac{10}{x}$ then $x =$ _____.

Answer 1

For incoherent waves:

$I_1 = I_A + I_B = I_0 + 9I_0 = 10I_0$

For coherent waves:

$I_2 = I_A + I_B + 2\sqrt{I_A I_B} \cos 60^\circ$ $I_2 = I_0 + 9I_0 + 2\sqrt{I_0 \times 9I_0} \cdot \frac{1}{2} = 13I_0$

Given:

$\frac{I_1}{I_2} = \frac{10}{13}$

Thus:

$x = 13$