question_answer

In a young’s double slit experiment, the slits are placed 0.320 mm apart. Light of wavelength \[\lambda \text{ }=\text{ }500\text{ }nm\] is incident on the slits. The total number of bright fringes that are observed in the angular range \[-30{}^\circ \le \,\theta \le 30{}^\circ \] is: [JEE Main 09-Jan-2019 Evening]

A)  640                 

B)       641

C)  320                  D)       321 Correct Answer: B Solution : [b] \[d\,sin\,\theta =n\,\lambda \]

\[0.320\,\times \,{{10}^{-3}}.\,\sin 30{}^\circ =n.500\,\,\times \,\,{{10}^{-9}}\]

\[n\,\,=\,\,\frac{320\,\,\times \,{{10}^{-6}}}{500\,\times \,{{10}^{-9}}}\,\,\times \,\frac{1}{2}\,\,=\,\,\frac{16}{50}\,\times \,1000\,=\,320\]

So, total no. of bright fringes

\[=\text{ }2\left( 320 \right)+1=641\]