What is the slit spacing of a diffraction grating necessary so that $600 - \mathrm { nm }$ light will produce a first order principal maximum at $25.0 ^ { \circ }$ away from the centerline?
A) $2.01 \mu \mathrm { m }$
B) $1.42 \mu \mathrm { m }$
C) $4.12 \mu \mathrm { m }$
D) $5.44 \mu \mathrm { m }$
E) $3.12 \mu \mathrm { m }$

Question

Quizplus · Accepted Answer

The slit spacing $d$ for a diffraction grating can be found using the formula for the angles of maxima, $d \sin \theta = m\lambda$, where $m$ is the order of the maximum, $\lambda$ is the wavelength of the light, and $\theta$ is the angle from the centerline. For the first order maximum ($m = 1$), with $\lambda = 600 \, \mathrm{nm} = 600 \times 10^{-9} \, \mathrm{m}$ and $\theta = 25.0^\circ$, solving for $d$ gives:$$d = \frac{\lambda}{\sin \theta} = \frac{600 \times 10^{-9}}{\sin(25.0^\circ)} \approx 1.42 \times 10^{-6} \, \mathrm{m} = 1.42 \, \mu\mathrm{m}$$

What Is the Slit Spacing of a Diffraction Grating Necessary 600−nm600 - \mathrm { nm }600−nm

What Is the Slit Spacing of a Diffraction Grating Necessary $600 - \mathrm { nm }$