Question

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

• 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

The correct option is D ${sin}^{-1}\left({3\times 10}^{-6}\right)$

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