First slide

Diffraction

Question

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?

Moderate

A

0.5 mm
B

0.02 mm
C

0.2 mm
D

0.1 mm

Solution

For double slit experiment,
$d = 1 mm = 1 \times 10^{- 3} m, D = 1 m, λ = 500 \times 10^{- 9} m$
$Fringe width β = \frac{D λ}{d}$
$Width of central maxima in a single slit = \frac{2 λ D}{a}$
As per question, width of central maxima of single slit pattern = width of 10 maxima of double slit pattern
$\frac{2 λ D}{a} = 10 (\frac{λ D}{d})$
$a = \frac{2 d}{10} = \frac{2 \times 10^{- 3}}{10} = 0.2 \times 10^{- 3} m = 0.2 mm$

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