A laser beam is directed through a grating and a first-order maximum is produced at 17°. What is the highest order maximum that can be produced by this arrangement?
A) 2
B) 3
C) 4
D) 5
E) 6

Question

Quizplus · Accepted Answer

The highest order maximum, $m$, for a diffraction grating can be found using the grating equation $d\sin(\theta) = m\lambda$, where $d$ is the grating spacing, $\theta$ is the diffraction angle, and $\lambda$ is the wavelength of the light. Since the first-order maximum ($m=1$) occurs at 17°, for higher orders, the angle must increase. However, the sine function has a maximum value of 1, corresponding to an angle of 90°. Therefore, to find the highest possible order, we set $\sin(\theta) = 1$, which gives $d\sin(90°) = m\lambda$. Since $d\sin(17°) = \lambda$ for the first order, by increasing the angle to 90°, we are essentially finding how many times $\lambda$ can fit into $d\sin(90°)$ or equivalently, how many times the first-order condition can be met within the physical constraints of the sine function. Given that $\sin(17°)$ is significantly less than 1, and considering the discrete nature of $m$, the highest order achievable before exceeding the sine function's maximum is 3, as going to the fourth order would require a sine value greater than 1, which is impossible.

A Laser Beam Is Directed Through a Grating and a First-Order