When light illuminates a diffraction grating with 7000 lines per centimeter, its second order maximum is at $62.4 ^ { \circ }$. What is the wavelength of the light?
A) $363 \mathrm {~nm}$
B) $336 \mathrm {~nm}$
C) $633 \mathrm {~nm}$
D) $752 \mathrm {~nm}$

Question

Quizplus · Accepted Answer

The wavelength of the light can be found using the diffraction grating equation $d \sin \theta = m\lambda$, where $d$ is the grating spacing, $\theta$ is the angle of the diffraction order, $m$ is the order number, and $\lambda$ is the wavelength. Given 7000 lines per centimeter, the spacing $d = \frac{1}{7000} \text{ cm} = \frac{1}{700000} \text{ m}$. For the second order maximum ($m = 2$) at $62.4^\circ$, solving for $\lambda$ gives $\lambda = \frac{d \sin \theta}{m}$. Substituting the given values, $\lambda \approx 633 \mathrm {~nm}$.

When Light Illuminates a Diffraction Grating with 7000 Lines Per 62.4∘62.4 ^ { \circ }62.4∘

When Light Illuminates a Diffraction Grating with 7000 Lines Per $62.4 ^ { \circ }$