In a double slit experiment, the two slits are 1 mm apart and the screen is placed 1 m away. A monochromatic light of wavelength 500 nm is used. What will be the width of each slit for obtaining ten maxima of double slit within the central maxima of single slit pattern?

 

Given distance between slits, d = 1 mm
Distance between slits and screen, D = 1 m.
Wavelength of light $\lambda$=500 nm.
In diffraction, width of central maxima
$=2\frac{D\lambda }{a}$
Where ‘a’ is slit width.
But is is given that
Width of central maxima of diffraction = 10 maxima of double slit.
$\begin{array}{l}\therefore 2.\frac{D\lambda }{a}=10.\beta \\ \frac{2D\lambda }{a}=10.\frac{D\lambda }{d};\because \beta =\frac{D\lambda }{d}\\ \Rightarrow a=\frac{2\times d}{10}=\frac{2\times 1}{10}=0.2\mathrm{mm}.\end{array}$