Question

In an interference experiment, the spacing between successive maxima or minima is

• A. $\frac{\mu d}{D}$
• B. $\frac{\lambda D}{d}$
• C. $\frac{dD}{\lambda \mu }$
• D. $\frac{\mu \lambda }{4D}$

Answer 1

The correct option is B

$\frac{\lambda D}{d}$

Step 1: Understand Young’s Double Slit Experiment

Young’s Double Slit Experiment:

1. Young's double slit experiment used diffracted light of a single source from two slits to produce two coherent sources.
2. Because the waves must have a constant phase difference, the two slits do not have to be symmetrically positioned from the first slit to produce an interference pattern.

Step 2: Understand Fringe width

1. The interference pattern produced by the double-slit experiment is made up of alternate light and dark fringes that run parallel to the slits.
2. The fringe width is the distance between two successive bright or dark fringes.
3. The core brilliant fringe is the fringe generated in the center of the fringe design.

Step 3: Find Fringe width in Interference

Mathematical Expression for fringe width ($\mathrm{\beta }$):-

1. For dark fringe: $x_n=\frac{n\lambda D}{d}$
2. For light fringe: $x_{n+1}=\frac{(n+1)\lambda D}{d}$
3. Now, the fringe width is the distance between consecutive dark and bright fringes. So, mathematically it can be expressed as

$$\begin{gathered} \beta =x_{n+1}-x_n \\ \beta =\frac{(n+1)\lambda D}{d}-\frac{n\lambda D}{d} \\ \beta =\frac{\lambda D}{d} \end{gathered}$$

The spacing between successive maxima or minima is $\frac{\lambda D}{d}$

Hence, option B is correct.