question_answer

A beam of light of \[\lambda =600\,nm\] 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 first dark fringes on either side of the central bright fringe is                                                                                                                                [NEET 2014]

A)  1.2 cm

B)       1.2 cm

C)  2.4 cm            

D)  2.4 cm

Correct Answer: D

Solution :

From the figure, \[\tan \theta =\frac{x/2}{2}\]

For small \[\theta \] and when \[\theta \] is counted in rad, \[\tan \simeq \theta \]

So,       \[\theta \simeq \frac{x/2}{2}\Rightarrow \frac{\lambda }{9}\simeq \frac{x}{4}\]

\[x\simeq \frac{4\lambda }{a}\simeq \frac{4\times 600\times {{10}^{-9}}}{{{10}^{-3}}}m\]

\[\simeq 24\times {{10}^{-4}}m\]

\[\simeq 2.4\times {{10}^{-3}}m\]

\[\simeq 2.4\,mm\]