Diffraction grating: Monochromatic light is incident on a grating that is 75 mm wide and ruled with 50,000 lines. The second-order maximum is seen at 32.5°. What is the wavelength of the incident light?
A) 202 nm
B) 403 nm
C) 452 nm
D) 605 nm
E) 806 nm

Question

Quizplus · Accepted Answer

The wavelength ($\lambda$) can be found using the diffraction grating equation $\lambda = \frac{d \sin \theta}{m}$, where $d$ is the grating spacing (the inverse of the number of lines per meter), $\theta$ is the angle of the diffraction order, and $m$ is the order number. Given 50,000 lines per 75 mm, or 50,000 lines per 0.075 m, the spacing $d = \frac{1}{50000/0.075} = \frac{0.075}{50000}$ meters. For the second-order maximum ($m = 2$) at 32.5°, $\lambda = \frac{(0.075/50000) \sin(32.5°)}{2}$. Calculating gives a wavelength close to 403 nm.

Diffraction Grating: Monochromatic Light Is Incident on a Grating That