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In Young's double slit experiment the separation d between the slits is 2 mm, the wavelength $\lambda$ of the light used is 5896 Å and distance D between the screen and slits is 100 cm. It is found that the angular width of the fringes is $0.20^\circ$. To increase the fringe angular width to $0.21^\circ$ (with same $\lambda$ and D) the separation between the slits needs to be changed to
Explanation
Angular width $\lambda/d$ is inversely proportional to d.
Detailed Solution
Angular width $\theta = \frac{\lambda}{d}$
$0.20^\circ = \frac{\lambda}{2\ mm}$ ...(i)
$0.21^\circ = \frac{\lambda}{d}$ ...(ii)
Dividing, $\frac{0.20}{0.21} = \frac{d}{2\ mm}$
$\Rightarrow d = 1.9$ mm