Question

In Young's double slit experiment, the distance between the slits is reduced to half and the distance between the slit and the screen doubled. The fringe width

• A. will become one fourth
• B. will become half
• C. will be doubled
• D. will become four times

Answer 1

The correct option is D will become four times

The fringe width is given by,
$\beta =\frac{\lambda D}{d}...\left(1\right)$

Distance between the slits is reduced to half i.e $\frac{d}{2}$ and distance between the slit and screen is doubled i.e $2D$.

So, ${\beta }^{\prime }=\frac{\lambda 2D}{\frac{d}{2}}=\left(\frac{\lambda D}{d}\right)4...\left(2\right)$

On comparing equations $\left(1\right)$ & $\left(2\right)$, we get ${\beta }^{\prime }=4\beta$
i.e. the fringe width becomes four times.

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