What is the slit spacing of a diffraction grating necessary so that 600-nm light will produce a first order principal maximum at 25.0° away from the centerline?
A)1.42 μm
B)2.01 μm
C)3.12 μm
D)4.12 μm
E)5.44 μm

Question

Quizplus · Accepted Answer

The slit spacing $d$ of a diffraction grating can be found using the formula for the maxima in diffraction, $d\sin(\theta) = m\lambda$, where $d$ is the slit spacing, $\theta$ 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 ($m = 1$), with $\lambda = 600$ nm (or $600 \times 10^{-9}$ m) and $\theta = 25.0^\circ$, the equation becomes $d\sin(25.0^\circ) = 1 \times 600 \times 10^{-9}$ m. Solving for $d$ gives a value close to $1.42 \times 10^{-6}$ m or $1.42$ μm.

What Is the Slit Spacing of a Diffraction Grating Necessary