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 [AIPMT 2014]

A)  1.2 cm

B)  1.2 mm

C)  2.4 cm

D)  2.4 mm

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,   \[\theta \simeq \frac{x/2}{2}\Rightarrow \frac{\lambda }{9}\simeq \frac{x}{4}\] \[x\simeq \frac{4\lambda }{a}\simeq \frac{4\times 600\times {{10}^{-9}}}{{{10}^{-3}}}m\] \[\simeq 24\times {{10}^{-4}}m\] \[\simeq 2.4\times {{10}^{-3}}m\] \[\simeq 2.4mm\]