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 calculated using the grating equation for diffraction maxima, $\lambda = \frac{d \sin \theta}{m}$, where $d$ is the grating spacing (the distance between adjacent lines), $\theta$ is the diffraction angle, and $m$ is the order of the maximum. Given that the grating is 75 mm wide and has 50,000 lines, the spacing $d = \frac{75 mm}{50,000} = 1.5 \times 10^{-3} mm = 1.5 \times 10^{-6} m$. For the second-order maximum ($m = 2$) at $32.5°$, $\lambda = \frac{1.5 \times 10^{-6} m \times \sin(32.5°)}{2}$. Calculating this gives a wavelength close to 403 nm.

Monochromatic Light Is Incident on a Grating That Is 75