A diffraction grating has $1250$ lines per millimetre. Monochromatic light of wavelength $650,\text{nm}$ falls normally on the grating. Find the angle at which the first order ($m=1$) maximum is observed.

Step-by-step solution

1. $d=\frac{1}{\text{lines per metre}}$ gives the grating spacing.
2. $1250\text{lines/mm}=1.25\times 10^6\text{lines/m}$ so $d=\frac{1}{1.25\times 10^6}=8.0\times 10^{-7},\text{m}$ (0.8 µm).
3. "For a grating, $sin\theta =mlambda/d$. With $m=1$, $\lambda =650,\text{nm}=6.5\times 10^{-7},\text{m}$, $sin\theta =\frac{6.5\times 10^{-7}}{8.0\times 10^{-7}}=0.8125$.
4. "$\theta =\arcsin (0.8125)\approx 54.1^{\circ }$.
5. "Thus the first‑order maximum appears at about $54^{circ}$ relative to the normal.

Concept tested: Diffraction by a grating

Published 16 September 2026 · How this solution was prepared and checked