At what angle will the fourth-order maximum occur for a wavelength of 513 nm using a diffraction grating with 10 890 lines per cm?
A)30°
B)90°
C)No fourth-order maximum will occur in this case.
D)1.6°
E)12.8°

Question

Quizplus · Accepted Answer

The angle for a maximum in a diffraction grating is given by the equation $d\sin(\theta) = m\lambda$, where $d$ is the grating spacing, $m$ is the order of the maximum, and $\lambda$ is the wavelength. The grating spacing $d$ can be found from the number of lines per cm, which is $10,890$ lines/cm or $108,900$ lines/m, giving $d = \frac{1}{108,900}$ m. For the fourth-order maximum ($m=4$) and $\lambda = 513$ nm or $513 \times 10^{-9}$ m, substituting these values into the equation would result in $\sin(\theta)$ being greater than 1, which is impossible, indicating that a fourth-order maximum cannot occur with these parameters.

At What Angle Will the Fourth-Order Maximum Occur for a Wavelength