The distance between the ruled lines on a diffraction grating is $1770 \mathrm {~nm}$. The grating is illuminated at normal incidence with a parallel beam of white light in the $400 \mathrm {~nm}$ to $700 \mathrm {~nm}$ wavelength band. What is the longest wavelength that appears in the third order spectrum?
A) $590 \mathrm {~nm}$
B) $570 \mathrm {~nm}$
C) $530 \mathrm {~nm}$
D) $610 \mathrm {~nm}$
E) $550 \mathrm {~nm}$

Question

Quizplus · Accepted Answer

The longest wavelength in the third order spectrum is found using the grating equation $d \sin \theta = m \lambda$. For the maximum wavelength, $\sin \theta$ should be 1. Thus, $1770 \, \text{nm} = 3 \lambda$, giving $\lambda = 590 \, \text{nm}$.

The Distance Between the Ruled Lines on a Diffraction Grating 1770 nm1770 \mathrm {~nm}1770 nm

The Distance Between the Ruled Lines on a Diffraction Grating $1770 \mathrm {~nm}$