Question

Two slits are separated by $0.3\text{mm}$. A beam of $500\text{nm}$ light strikes the slits, producing an interference pattern. The number of maxima observed in the angular range $-{30}^{\circ }<\theta <{30}^{\circ }$.

• A. $299$
• B. $399$
• C. $499$
• D. $599$

Answer 1

The correct option is D $599$

We know, for maximum, the path difference is given by

$d\sin \theta =n\lambda$

$\Rightarrow 0.3\times {10}^{-3}\times \sin {30}^{\circ }=n\times 500\times {10}^{-9}$

$\Rightarrow n=\frac{1000\times 3}{10}$

$\Rightarrow n=300$

For, $0^{\circ }<\theta \le {30}^{\circ };n=300$

Similarly, for $-{30}^{\circ }\le \theta <0^{\circ };n=300$

$\therefore$ The total number of maxima observed in the angular range $-{30}^{\circ }\le \theta \le {30}^{\circ }$ including $0^{\circ }$,

$n_{total}=(2\times 300)+1=601$

But for $-{30}^{\circ }<\theta <{30}^{\circ }$,

$\Rightarrow n=601-2=599$

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