A monochromatic light is incident on a single slit of width $0.014 \mathrm{~mm}$. The angular position of…
A monochromatic light is incident on a single slit of width $0.014 \mathrm{~mm}$. The angular position of the second bright line observed is $2.81^{\circ}$. Then the wavelength of the incident light is $\left[\sin \left(2.81^{\circ}\right)=0.049072\right]$
$4026 Å$
$5890 Å$
$6040 Å$
$2748 Å$
Solution
We have for $n^{\text {th }}$ maxima
$a \sin \theta=(2 n+1) \frac{\lambda}{2}$
$\begin{aligned} & \Rightarrow \lambda=\frac{2 \mathrm{a} \sin \theta}{(2 \mathrm{n}+1)} \\ & \Rightarrow \lambda=\frac{2 \times 0.014 \times 10^{-3} \times \sin (2.81)}{(2 \times 2+1)} \\ & =2748 Å\end{aligned}$