Question

In a Young's double slit experiment, the slits are placed $0.320\text{mm}$ apart. Light of wavelength $\lambda =500\text{nm}$ 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

• A. $641$
• B. $321$
• C. $320$
• D. $640$

Answer 1

The correct option is A $641$

For ${}^{\prime }{n}^{\prime }$ number of maxima,

$d\sin \theta =n\lambda$
For, $0<\theta \le {30}^{\circ }$

$0.32\times {10}^{-3}\sin {30}^{\circ }=n_1\times 500\times {10}^{-9}$

$n_1=\frac{0.32\times {10}^{-3}}{500\times {10}^{-9}}\times \frac{1}{2}=320$

Similarly, for $-{30}^{\circ }\le \theta <0$

$n_2=320$

There will be one more bright fringe at center.

Therefore, total number of maxima observed in angular range $-{30}^{\circ }\le \theta \le {30}^{\circ }$ is ,

$n=320+1+320=641$

Hence, option $\left(D\right)$ is correct.