A helium-neon laser (λ = 632.8 nm) is used to calibrate a diffraction grating. If the first-order maximum occurs at 20.5°, what is the line spacing, d? A) 1.81 × 10−⁶ m B) 1.00 × 10−⁵ m C) 1.00 × 10−⁴ m D) 1.31 × 10−⁶ m E) 6.76 × 10−⁷ m

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Quizplus · Accepted Answer

The line spacing, $d$, of a diffraction grating can be calculated using the formula $d \sin(\theta) = m\lambda$, where $\theta$ is the angle of the diffraction maximum, $m$ is the order of the maximum, and $\lambda$ is the wavelength of the light. For the first-order maximum ($m = 1$) at $20.5^\circ$ with $\lambda = 632.8 \, \text{nm} = 632.8 \times 10^{-9} \, \text{m}$, solving for $d$ gives:$$d = \frac{\lambda}{\sin(\theta)} = \frac{632.8 \times 10^{-9}}{\sin(20.5^\circ)} \approx 1.81 \times 10^{-6} \, \text{m}$$

A Helium-Neon Laser (λ = 632