Question

Find the angular width between the first maxima on either sides of the central maxima. The double slit experiment is performed with light of wavelength $3\times {10}^{-6}\text{m}$ and the separation between the slits is $6\mu \text{m}$,

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${90}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

The correct option is B ${60}^{\circ }$

Given,
$\lambda =3\times {10}^{-6}\text{m}$
$d=6\mu m=6\times {10}^{-6}\text{m}$

Angular position of first maxima,
$\sin \theta =\frac{\lambda }{d}=\frac{30\times {10}^{-6}}{6\times {10}^{-6}}=\frac{1}{2}$
$\therefore \theta ={30}^{\circ }$

Now, angular width between the first maxima on either side of central maxima$=2\theta ={60}^{\circ }$

Hence, $\left(B\right)$ is the correct answer.

$\begin{array}{c}\text{Why this question?}\\ \text{Caution:While using formula d sin}\theta =\lambda ,\\ \text{use approximation only when value of sin}\theta \\ \text{is very small.}\end{array}$