Question

Two coherent sources emit light of wavelength $\lambda$. separation between, $d=4\lambda$. If a detector moves along the y-axis, what is the maximum number of minima observed?

• A. $6$
• B. $8$
• C. $5$
• D. $4$

Answer 1

The correct option is B $8$

Given : path difference,$\Delta x=dsin\theta =4\lambda$

For minima, $\Delta x=(n+\frac{1}{2})\lambda$

Thus, $dsin\theta =(n+\frac{1}{2})\lambda$

$4\lambda sin\theta =(n+\frac{1}{2})\lambda$

$⟹sin\theta =(n+\frac{1}{2})\frac{1}{4}$

But as $-1\le sin\theta \le 1$ ......................(1)

For $n=-4,-3,-2,-1,0,1,2,3$ satisfy (1), hence there will be only $8$ minimas to be observed.