Question

Two coherent sources of light $S_1\text{and}{S}_2$, equidistant from the origin, are separated by a distance $2\lambda$ as shown. They emit light of wavelength $\lambda$. Interference is observed on a screen placed along a large circle of radius $R$. A point on the circumference is found to be a point of constructive interference. Then angle $\theta$ (in the first quadrant of the circle) is,
(Consider that the vertical diameter is the point where central bright fringe lies)

• A. ${45}^{\circ }$
• B. ${30}^{\circ }$
• C. ${60}^{\circ }$
• D. $\text{Not possible in the first quadrant}$

Answer 1

The correct option is C ${60}^{\circ }$



$\Delta x=d\cos \theta =n\lambda$ (for maxima)

$\cos \theta =\frac{n\lambda }{d}\Rightarrow \cos \theta =\frac{n}{2}$

For maxima, $n=1$

$\Rightarrow \theta ={60}^{\circ }$

Hence, $\left(C\right)$ is the correct answer.