Two coherent monochromatic light beams of intensities 4I and 9I are superimposed. If the difference between maximum and minimum intensities in the interference pattern is xI, find x.
Physics · Wave Optics · Huygens' Principle & Interference of Light
JEE Mains 2025 3 April Morning Shift

Question

Two coherent monochromatic light beams of intensities 4I and 9I are superimposed. If the difference between maximum and minimum intensities in the interference pattern is xI, find x.

G1 Physics · Accepted Answer

For two coherent beams, I m a x I_max I m ​ a x = (√I₁ + √I₂)², I m i n I_min I m ​ in = (√I₁ - √I₂)². Here, I₁ = 4I, I₂ = 9I. Therefore, I m a x I_max I m ​ a x = (2√I + 3√I)² = 25I. And, I m i n I_min I m ​ in = (3√I - 2√I)² = I. Hence, I m a x I_max I m ​ a x - I m i n I_min I m ​ in = 25I - I = 24I. Thus x = 24.