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?

Question

Quizplus · Accepted Answer

The wavelength ($\lambda$) can be calculated using the 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 maximum, and $m$ is the order of the maximum. Given that the grating is 75 mm wide with 50,000 lines, the spacing $d = \frac{75 \times 10^{-3}}{50000} = 1.5 \times 10^{-6}$ m. For the second-order maximum ($m = 2$) at 32.5°, $\lambda = \frac{1.5 \times 10^{-6} \sin(32.5°)}{2}$, which calculates to approximately 403 nm.

Monochromatic Light Is Incident on a Grating That Is 75