Q: Two coherent monochromatic light beams of intensities I and 4I are superposed. The maximum and minimum possible intensities in the resulting beam are
(A) 5I and I
(B) 5I and 3I
(C) 9I and I
(D) 9I and 3I.
Ans: (C)
Sol: using formula
$\large I = I_1 + I_2 + 2 \sqrt{I_1 I_2 } cos\phi $
I1 = I , I2 = 4I
$\large I_{max} = (\sqrt{I_1} + \sqrt{I_2})^2$ , when φ = 0°
$\large I_{max} = (\sqrt{I} + \sqrt{4I})^2 = 9 I$
$\large I_{min} = (\sqrt{I_1} – \sqrt{I_2})^2$ , when φ = 180°
$\large I_{min} = (\sqrt{I} – \sqrt{4I})^2 = I$