Question

Suppose an experiment where a monochromatic light is passed through $3$ slits as shown in the figure. $($Consider $3$ parallel rays as shown from the $3$ slits$)$ What is the path difference between rays number $1$ and $3$?

• A. $d\sin \theta$
• B. $2d\sin \theta$
• C. $d\cos \theta$
• D. $2d\cos \theta$

Answer 1

The correct option is B $2d\sin \theta$


$CD$ is the path difference between rays number $1$ and $3$.
Here, $\angle CAD=\theta$
and $AC=2d$
In $\Delta ADC,\angle ADC={90}^{\circ }$
Hence, $CD=AC\sin \theta =2d\sin \theta$

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

$\begin{array}{c}\text{Why this question?}\\ \text{Note :- For multiple slit interference the path difference between parallel rays progresses as}d\sin \theta ,2d\sin \theta ,3d\sin \theta ....\end{array}$