Question

In the Youngs experiment with sodium light, the slits are $0.589m$ apart. What is the angular separation of the third maximum from the central maximum? Given that $\lambda =589nm.$

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

Answer 1

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

Using relation,

$d\sin \theta =n\lambda$

$\Rightarrow \sin \theta =\frac{n\lambda }{d}$

For third maximum ,

$n=3$

$\therefore \sin \theta =\frac{3\pi }{d}$

$\Rightarrow \sin \theta =\frac{3\times 589\times {10}^{-9}}{0.589}$

$\Rightarrow \sin \theta =3\times {10}^{-6}$

$\Rightarrow \theta ={\sin }^{-1}(3\times {10}^{-6})$