When a diffraction grating having 5000 lines/cmis illuminated by monochromatic light, the angle between the central maximum and the fourth order maximum is $47.2 ^ { \circ }$. What is the wavelength of the light?
A) $367 \mathrm {~nm}$
B) $637 \mathrm {~nm}$
C) $183 \mathrm {~nm}$
D) $138 \mathrm {~nm}$

Question

Quizplus · Accepted Answer

The wavelength of the light can be calculated using the diffraction grating equation $d \sin \theta = m \lambda$, where $d$ is the grating spacing, $\theta$ is the diffraction angle, $m$ is the order of the maximum, and $\lambda$ is the wavelength of the light. Given 5000 lines/cm, the spacing $d = 1/5000$ cm = $2 \times 10^{-4}$ cm = $2 \times 10^{-6}$ m. For the fourth order maximum ($m = 4$) and $\theta = 47.2^\circ$, substituting these values into the equation gives $\lambda = \frac{d \sin \theta}{m}$. Calculating this yields a wavelength of approximately $367 \mathrm{nm}$.

When a Diffraction Grating Having 5000 Lines/cmis Illuminated by Monochromatic 47.2∘47.2 ^ { \circ }47.2∘

When a Diffraction Grating Having 5000 Lines/cmis Illuminated by Monochromatic $47.2 ^ { \circ }$