Question

The slit width, when a light of wavelength $ 6500\,\mathring{A}$ is incident on a slit, if first minima for red light is at $30^{\circ}$, is:

• A. $ 1\times 10^{-6}\,m $
• B. $ 5.2\times 10^{-6}\,m $
• C. $ 1.3\times 10^{-6}\,m $
• D. $ 2.6\times 10^{-6}\,m $

Answer 1

Answer: (C)

When rays of monochromatic light of wavelength $\lambda$ are incident on a diffraction grating in which slit separation is $d$,
then for angle of diffraction $\theta$ ,
the following relation holds true.
$d \sin \theta=n \lambda$
where $n$ is called the spectrum order.
Given, $n =1, \lambda=6500\,\mathring{A}=6500 \times 10^{-10}m$
and $\sin 30^{\circ}=\frac{1}{2}$
$\Rightarrow d=\frac{n \lambda}{\sin 30^{\circ}}$
$\therefore d=\frac{6500 \times 10^{-10}}{(1 / 2)}$
$d=1.3 \times 10^{-6} m$