Monochromatic light from a He-Ne laser (λ = 632.8 nm) is incident on a diffraction grating containing 5000 lines/cm. Determine the angle of the first-order maximum.
A) 18.4°
B) 39.2°
C) 14.6°
D) 27.7°
E) 13.9°

Question

Quizplus · Accepted Answer

The angle of the first-order maximum for a diffraction grating can be found using the formula $d\sin\theta = m\lambda$, where $d$ is the grating spacing, $m$ is the order of the maximum, and $\lambda$ is the wavelength of the light. Given 5000 lines/cm, the spacing $d = \frac{1}{5000\, \text{lines/cm}} = \frac{1}{500000\, \text{lines/m}} = 2 \times 10^{-6}\, \text{m}$. For the first-order maximum ($m = 1$) and $\lambda = 632.8 \, \text{nm} = 632.8 \times 10^{-9}\, \text{m}$, substituting these values into the formula gives $\sin\theta = \frac{632.8 \times 10^{-9}}{2 \times 10^{-6}}$, solving for $\theta$ gives $\theta \approx 18.4^\circ$.

Monochromatic Light from a He-Ne Laser (λ = 632