Diffraction grating: What is the angular separation of the two second-order spectral lines having wavelengths 417 nm and 388 nm using a diffraction grating having 456 lines/mm?
A) 1.63°
B) 1.52°
C) 0.815°
D) 3.26°

Question

Quizplus · Accepted Answer

The angular separation can be calculated using the grating equation $d\sin\theta = m\lambda$, where $d$ is the grating spacing, $m$ is the order of the spectrum, and $\lambda$ is the wavelength. The grating spacing $d$ is the reciprocal of the number of lines per meter, so for 456 lines/mm, $d = \frac{1}{456 \times 10^3}$ meters. For the second order ($m = 2$), the difference in angles for the two wavelengths can be found and converted to degrees, resulting in an angular separation of approximately 1.63°.

Diffraction Grating: What Is the Angular Separation of the Two