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  4. Fraunhofer diffraction pattern of a single slit is obtained in the focal plane of the lens of focal length 1 m . If the third minimum is formed at a distance of 5 mm from the central maximum and wavelength of light used is 5000 overset° A , then the width of the slit will be

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Q. Fraunhofer diffraction pattern of a single slit is obtained in the focal plane of the lens of focal length $1 \, m$ . If the third minimum is formed at a distance of $5 \, mm$ from the central maximum and wavelength of light used is $5000 \, \overset{^\circ }{A}$ , then the width of the slit will be

NTA AbhyasNTA Abhyas 2020Wave Optics

Solution:

Using $asin \theta =n\lambda $
Or $a \, . \, \frac{x}{f}=3\lambda $ or $a=\frac{3 \lambda \, . \, \, f}{x}$
$=\frac{3 \times 500 \times 10^{- 9} \times 1}{5 \times 10^{- 3}}=3\times 10^{- 4} \, m=0.03 \, cm$