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Q.

In Young's double-slit experiment, the separation between the two slits is $2.0 mm$ . What should be the width of each slit (in mm) so as to accommodate 10 maxima of the double-slit experiment within the central maximum of the single slit diffraction experiment?

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Detailed Solution

In Young's double-slit experiment, the angular separation between 10 maxima is
$θ_{1} = \frac{10 λ}{d}$
In single slit diffraction experiment, the angular width of the central maximum is
$θ_{2} = \frac{2 λ}{a}, (a = w i d t h o f e a c h s l i t)$
Given $θ_{1} = θ_{2}$ , which requires
$\frac{10 λ}{d} = \frac{2 λ}{a}$
$\Rightarrow a = \frac{2 d}{10} = \frac{2 \times 2 mm}{10} = 0.4 mm$

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