Answer to Question #99325 in Optics for Ra

Question

To calculate the angle of diffraction for red colour(λ=8000 angstrom)in the first order of spectrum for a grating with 14438 lines per inch.

Answer 1

Condition for $m^{th}$ interference maximum is $d sin \theta = m \lambda$, where $d$ is slit separation and $\lambda$ is the wavelength.

We are given grating $N = 14438\frac{lines}{inch}$, from where the slit separation is $d = \frac{1}{N} = 6.926 inch= 1.759 \cdot 10^{-6} m$. The wavelength is $\lambda = 8000A = 800nm$.

Hence, for the first maximum, $\sin \theta = \frac{\lambda}{d} \approx 0.455$, which corresponds to $\theta \approx 27^{\circ}$.