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  • A beam of light of wave length 600 nm from a distant source falls on a single slit 1 mm wide and the resulting diffraction pattern is observed on a screen 2 m away. The distance between the first d

A beam of light of wave length 600 nm from a distant source falls on a single slit 1 mm wide and the resulting diffraction pattern is observed on a screen 2 m away. The distance between the first dark fringes on either side of the central bright is

Option: 1

1.2 \mathrm{~cm}


Option: 2

1.2 \mathrm{~mm}


Option: 3

2.4 \mathrm{~cm}


Option: 4

24 \mathrm{~mm}


Answers (1)

best_answer

For first minimum putting \mathrm{n}=1
in the condition for minima given as \mathrm{d \operatorname{Sin} \theta=n \lambda}
we obtain \mathrm{d \sin \theta=\lambda \quad \ldots(1)}


\mathrm{where \, \sin \theta \cong \theta \cong \frac{x / 2}{D}}
\mathrm{\Rightarrow \quad \sin \theta=\frac{\mathrm{x}}{2 \mathrm{D}}}\quad \ldots(2)

using (1) and (2) we obtain,
\mathrm{\frac{\lambda}{\mathrm{d}}=\frac{\mathrm{x}}{2 \mathrm{D}}}
\mathrm{x=\frac{2 \lambda D}{d}=\frac{2\left(600 \times 10^{-9}\right)(2)}{10^{-3}}}
\mathrm{=2.4 \times 10^{-3} \mathrm{~m}}
\mathrm{=2.4 \mathrm{~mm}}
 

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vinayak

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