Q: In the young’s double slit experiment using a monochromatic light of wavelength λ , the path difference (in terms of an integer n) corresponding to any point having half the peak intensity is :

(A) $\large (2n+1)\frac{\lambda}{2}$

(B) $\large (2n+1)\frac{\lambda}{4}$

(C) $\large (2n+1)\frac{\lambda}{8}$

(D) $\large (2n+1)\frac{\lambda}{16}$

**Solution :**

$\large I = I_{max} cos^2 \frac{\phi}{2}$ …(i)

Given $\large I = \frac{I_{max}}{2}$ …(ii)

From (i) & (ii)

$\large \phi = \frac{\pi}{2} , \frac{3\pi}{2} , \frac{5\pi}{2}$

Path difference $\large \Delta x = \frac{\lambda}{2\pi}.\phi $

$\large \Delta x = \frac{\lambda}{4} , \frac{3\lambda}{4} , \frac{5\lambda}{4} …(2n+1)\frac{\lambda}{4}$

Correct option is (B)