# Two coherent monochromatic light beams of intensities I and 4I are superposed…

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°

$\large I_{min} = (\sqrt{I} – \sqrt{4I})^2 = I$