Question

Light of wavelength $5000 \,?$ is incident normally on a slit of width $2.5 \times 10^{-4} \, cm$. The angular position of second minimum from the central maximum is

• A. $\sin^{-1} \left(\frac{1}{5}\right)$
• B. $\sin^{-1} \left(\frac{2}{5}\right)$
• C. $\left(\frac{\pi}{3}\right)$
• D. $\left(\frac{\pi}{6}\right)$

Answer 1

The Correct Option is B

We know that,
Angular width of central maximum $=\frac{2 \lambda}{a}$
where, $\lambda=$ wavelength of light,
$a=$ width of single slit,
So, $ \sin \theta=\frac{2 \lambda}{a} $
where $ \lambda =5000\, ?=5000 \times 10^{-10}\, m$
$a =2.5 \times 10^{-6} m $
$\Rightarrow \sin \theta =\frac{2 \times 5000 \times 10^{-10}}{2.5 \times 10^{-6}} $
$\sin \,\theta =\frac{100000 \times 10^{-10}}{25 \times 10^{-6}} $
$\sin \,\theta =\frac{10 \times 10^{10} \times 10^{-10}}{25} $
$\sin \,\theta =\frac{10}{25} $
$\theta =\sin ^{-1}\left(\frac{2}{5}\right) $