Question

Two coherent sources emit light of wavelength $\lambda$. separation between, $d=4\lambda$. If the detector moves along the x-axis beginning from $S_2$, the maximum number of minima observed is :

• A. $2$
• B. $3$
• C. $5$
• D. $4$

Answer 1

The correct option is D $4$

Path difference between the two rays meeting at any point= $d\sin \theta$.

Now as the detector moves along x-axis beginning from $S_2$,

$\theta$ changes from $0^{\circ }$ to ${90}^{\circ }$.

For minima to be formed there, $d\sin \theta =(n+\frac{1}{2})\lambda$.

$d=4\lambda$

$⟹\sin \theta =(n+\frac{1}{2})\frac{1}{4}=\frac{1}{8},\frac{3}{8},\frac{5}{8},\frac{7}{8},\frac{9}{8}.....$

But since $\sin \theta <1$,

$sin\theta$ can take only 4 values.

Thus $\theta$ has only 4 values.

Therefore 4 minima are observed.