Question

In the Young's double slit experiment with sodium light, the slits are $0.589 \,m$ apart. The angular separation of the third maximum from the central maximum will be (given $\lambda=589 \,mm )$

• A. $\sin ^{-1}\left(0.33 \times 10^{8}\right)$
• B. $\sin ^{-1}\left(0.33 \times 10^{-6}\right)$
• C. $\sin ^{-1}\left(3 \times 10^{-8}\right)$
• D. $\sin ^{-1}\left(3 \times 10^{-6}\right)$

Answer 1

Answer: (D)

Using relation, $d \sin \theta=n \lambda \Rightarrow \sin \theta=\frac{n \lambda}{d}$
For $n=3, \sin \theta =\frac{3 \lambda}{d}=\frac{3 \times 589 \times 10^{-9}}{0.589} $
$=3 \times 10^{-6} \text { or } \theta=\sin ^{-1}\left(3 \times 10^{-6}\right) $