Question

Let $S_1$ and $S_2$ be the two slits in a Young's double slit experiment. If central maxima is observed at $P$ and $\angle S_{1}P{S}_2=\theta \left(\theta \text{is small}\right)$, find the $y-$coordinate of the third minima assuming the origin to be at the central maxima, $\lambda$ is the wavelength of light used.

• A. $\pm \frac{2\lambda }{\theta }$
• B. $\pm \frac{5\lambda }{2\theta }$
• C. $\pm \frac{3\lambda \theta }{2}$
• D. $\pm 2\lambda \theta$

Answer 1

The correct option is B $\pm \frac{5\lambda }{2\theta }$



As angle $\theta$ is small, we can write,
$\theta =\frac{d}{D}$

Let third minima is formed at point $Q$, at angular position $\theta {}^{\prime }$, as shown in the diagram.
Considering both the third minima, formed on both sides of point $P$, the $y$ coordinate of point of third minima is,
$\Rightarrow y=\pm \frac{5\beta }{2}=\pm \frac{5\lambda D}{2d}$
$=\pm \frac{5\lambda }{2\theta }(\because \theta =\frac{d}{D})$

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