What should be the slit width to obtain 10 maxima of the double slit pattern within the central maxima of the single slit pattern of distance between slit is 1mm.

0.4 mm 0.2 mm 0.6 mm 0.8 mm

0.2 mm

Let the width of each slit is $a$. Linear separation between $10$ fringes is given by $ x = 10\beta = \frac{10 \lambda D}{d}$ Angular separation is given by $\theta_1 = \frac{x}{d} = \frac{10\lambda}{d}$ Angular width of central maximum in the diffraction pattern of a single slit is given by  $\$\backslash theta\_2\; =\; \backslash frac\{2\backslash lambda\}\{a\}\$$ $\theta_2 = \theta_1$ $\frac{2\lambda}{a} = \frac{10\lambda}{d}$ $\Rightarrow a = \frac{2d}{10} = 0.2 d = 0.2 mm$​