AIIMS 2017 Physics Young's Double Slit Experiment MCQ Question

In Young's double slit experiment, the fringe width $\beta$ is given by the formula $\beta = \frac{\lambda D}{d}$, where $\lambda$ is the wavelength of light, $D$ is the distance from the slits to the screen, and $d$ is the separation between the slits. When the slit separation $d$ is halved and the distance $D$ is doubled, the new fringe width becomes $\beta' = \frac{\lambda (2D)}{(d/2)} = \frac{4\lambda D}{d} = 4\beta$, resulting in a fringe width that is four times larger than the original.

Options (A) and (B) are incorrect because they suggest changes in fringe width that do not align with the derived relationship, while option (C) is incorrect as it implies no change in fringe width despite the alterations in $d$ and $D$.