$(a)\;\frac{I}{2} \\ (b)\;\frac{I}{3} \\ (c)\;\frac{3I}{2} \\ (d)\;\frac{I}{4} $

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Path difference $\Delta =\large\frac{yd}{D}$

$d= 5 \lambda$

$D= 50 \lambda$

$y= \large\frac{d}{2}$

$\quad= \large\frac{5}{2}$$ \lambda$

$\therefore \Delta x= \large\frac{\lambda}{4}$

Corresponding phase difference $\phi$

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

$\qquad= \large\frac{2 \pi }{\lambda} \times \frac{\lambda}{4}$

$\qquad=\large\frac{\pi}{2}$

$\large\frac{\phi}{2} =\frac{\pi}{4}$

$I_1= I \cos^2 \large\frac{\phi}{2}$

$\qquad= I \cos^2 \large\frac{\pi}{4}$

$\qquad= I ( \large\frac{ 1}{\sqrt 2})^2$

$\qquad =\large\frac{ I}{2}$

Hence a is the correct answer.

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