A monochromatic light of wavelength 6000 is incident on the single slit of width 0.01 mm. If the diffraction pattern is formed at the focus of the convex lens of focal length 20 cm, the linear width of the central maximum is

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Solution

Q.
A monochromatic light of wavelength 6000 $Å$ is incident on the single slit of width 0.01 mm. If the diffraction pattern is formed at the focus of the convex lens of focal length 20 cm, the linear width of the central maximum is [2024]

1 60 mm

2 24 mm

3 120 mm

4 12 mm

Ans.
(2)

$Angular width = \frac{2 λ}{a}$

$Linear width = \frac{2 λ}{a} \cdot f$

$= \frac{2 \times 6000 \times 10^{- 10} \times 20 \times 10^{- 2}}{0.01 \times 10^{- 3}}$

$= 24 \times 10^{- 3} m = 24 mm$

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