The slit width, if first minima for red light is at 30⁰ when a light of wavelength 6500 $\stackrel{0}{\mathrm{A}}$ is incident on a slit, is

When rays of monochromatic light of wavelength $\lambda$ are incident on a single slit 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 $\stackrel{0}{\mathrm{A}}$ = 6500 X 10^-10 m

and  $\sin 30°=\frac{1}{2}$

$\Rightarrow d=\frac{n\lambda }{\sin 30°}=\frac{6500\times {10}^{-10}}{(1/2)}$

$\Rightarrow d=1.3\times {10}^{-6} \mathrm{m}$