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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
$\theta_2 = \frac{2\lambda}{a}$
$\theta_2 = \theta_1$
$\frac{2\lambda}{a} = \frac{10\lambda}{d}$
$\Rightarrow a = \frac{2d}{10} = 0.2 d = 0.2 mm$ |
