What is the slit spacing of a grating necessary so that 600-nm light will produce a first order principal maximum at 25.0° away from the centerline?

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Quizplus · Accepted Answer

The slit spacing $d$ can be found using the diffraction grating equation for the first order maximum ($m = 1$), which is $d \sin(\theta) = m\lambda$. Here, $\lambda = 600 \, \text{nm} = 600 \times 10^{-9} \, \text{m}$, $\theta = 25.0^\circ$, and $m = 1$. Solving for $d$ gives $d = \frac{\lambda}{\sin(\theta)}$. Plugging in the values, $d = \frac{600 \times 10^{-9}}{\sin(25^\circ)}$, which calculates to approximately $1.42 \, \mu\text{m}$.

What Is the Slit Spacing of a Grating Necessary So