A linear aperture whose width is 0.02 cm is placed immediately in front of a lens of focal length 60 cm. The aperture is illuminated normally by a parallel beam of wavelength . The distance of the first dark band of the diffraction pattern from the centre

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Solution

Q.
A linear aperture whose width is 0.02 cm is placed immediately in front of a lens of focal length 60 cm. The aperture is illuminated normally by a parallel beam of wavelength $5 \times 10^{- 5} cm$ . The distance of the first dark band of the diffraction pattern from the centre of the screen is [2016]

1 0.10 cm

2 0.25 cm

3 0.20 cm

4 0.15 cm

Ans.
(4)

Here, $a = 0.02$ $cm = 2 \times 10^{- 4}$ $m$

$λ = 5 \times 10^{- 5} cm = 5 \times 10^{- 7} m \Rightarrow D = 60 cm = 0.6 m$

Position of first minima on the diffraction pattern,

$y = \frac{D λ}{a} = \frac{0.6 \times 5 \times 10^{- 7}}{2 \times 10^{- 4}} = 15 \times 10^{- 4}$ $m = 0.15$ $cm$

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