Question

Figure shows two coherent sources $S_1$ and $S_2$ emitting wavelength $\lambda$. The separation $S_1{S}_2=1.5\lambda$ and $S_1$ is ahead in phase by $\pi /2$ relative $S_2$. Then the maxima occur in direction $\theta$ given by ${\sin }^{-1}$ of
$\left(i\right)0$; $\left(ii\right)1/2$; $\left(iii\right)-1/6$; $\left(iv\right)-5/6$
Correct options are:

• A. $\left(ii\right),\left(iii\right),\left(iv\right)$
• B. $\left(i\right),\left(ii\right),\left(iii\right)$
• C. $\left(i\right),\left(iii\right),\left(iv\right)$
• D. all of the above

Answer 1

Answer: (A)

$\left(ii\right),\left(iii\right),\left(iv\right)$

Since $S_1$ is ahead of $S_2$ by phase difference of $\pi /2$, the equivalent path difference between them is: $\frac{\pi }{2}\times \frac{\lambda }{2\pi }=\frac{\lambda }{4}$

Hence for constructive interference, $\frac{yd}{D}+\frac{\lambda }{4}=n\lambda$

$⟹d\sin \theta =(n-\frac{1}{4})\lambda$

Now, $d=1.5\lambda$, given.

Hence, $\sin \theta =\frac{2}{3}(n-\frac{1}{4})$

For $n=1,0,-1$

$\sin \theta =1/2,-1/6,-5/6$