Topic: Diffraction due to a single slit· Optics

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 5×10^-5 cm. The distance of the first dark band of the diffraction pattern…

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 \(5\times10^{-5}\) cm. The distance of the first dark band of the diffraction pattern from the centre of the screen is

1. 0.25 cm

2. 0.20 cm

3. 0.15 cm

4. 0.10 cm

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Answer: 3. 0.15 cm

For the first dark band in single-slit diffraction, \(a\sin\theta=\lambda\).

\(\sin\theta=\dfrac{5\times10^{-5}}{0.02}=2.5\times10^{-3}\), a small angle.
Distance on the screen (at the focal plane): \(y=f\tan\theta\approx f\sin\theta=60\times2.5\times10^{-3}=0.15\) cm.

Option (3).

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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 5×10^-5 cm. The distance of the first dark band of the diffraction pattern…

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