A diffraction grating has $6.00 \times 10 ^ { 3 }$ lines per centimeter ruled on it. What is the angular separation between the second and the third orders on the same side of the central order when the grating is illuminated with a beam of light of wavelength $550 \mathrm {~nm}$ ?
A) $50.5 ^ { \circ }$
B) $40.6 ^ { \circ }$
C) $30.5 ^ { \circ }$
D) $20.5 ^ { \circ }$

Question

Quizplus · Accepted Answer

The angular separation between two diffraction orders can be found using the grating equation $d \sin \theta = m \lambda$, where $d$ is the grating spacing, $\theta$ is the diffraction angle, $m$ is the order of the diffraction, and $\lambda$ is the wavelength of the light. The grating spacing $d$ is the reciprocal of the number of lines per meter, so for $6.00 \times 10^3$ lines per centimeter, $d = \frac{1}{6.00 \times 10^5}$ m. For the second order ($m=2$) and third order ($m=3$) using $\lambda = 550 \times 10^{-9}$ m, we calculate $\theta_2$ and $\theta_3$ and find their difference. The calculation shows that the angular separation corresponding to the given conditions is closest to $40.6^\circ$, making option B correct.

A Diffraction Grating Has 6.00×1036.00 \times 10 ^ { 3 }6.00×103

A Diffraction Grating Has $6.00 \times 10 ^ { 3 }$