16. In a double slit experiment, the two slits are 1 mm apart and the screen is placed 1 m away. A monochromatic light 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 ?

16. In a double slit experiment, the two slits are 1 mm apart and the screen is placed 1 m away. A monochromatic light 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 ?

(a) 0.1 mm

(b) 0.5 mm

(c) 0.02 mm

(d) 0.2 mm

Answer :  (d) 0.2 mm

\( 10 \beta \; \text{ of double slit } = 1 \text{ central bright of single slit } 2 \beta \)

 \( 10 \frac{\lambda D}{d} = 2 \frac{\lambda D}{a} \)

 \( a = \frac{2d}{10} = \frac{d}{5} = \frac{1 \,\text{mm}}{5} = 0.2 \,\text{mm} \)