The coherent monochromatic light beams of intensities 4I and 9I are superposed. What will be the maximum and minimum possible intensities?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 25I, I
For coherent beams the amplitudes add, so the resultant intensity is \( I = I_1+I_2+2\sqrt{I_1I_2}\cos\phi \). It is maximum for \( \cos\phi = +1 \) and minimum for \( \cos\phi = -1 \), giving \( (\sqrt{I_1}\pm\sqrt{I_2})^{2} \).
\( I_{\max} = \left(\sqrt{4I}+\sqrt{9I}\right)^{2} = (2+3)^{2}I = 25I \)
\( I_{\min} = \left(\sqrt{4I}-\sqrt{9I}\right)^{2} = (2-3)^{2}I = I \)