What slit separation would a grating have to produce a first-order maximum at an angle of 40.0$^{\circ}$for a wavelength of 589 nm?
A) 109 nm
B) 690 nm
C) 378 nm
D) 458 nm
E) 916 nm

Question

Quizplus · Accepted Answer

The grating equation is $d \sin \theta = m \lambda$, where $d$ is the slit separation, $\theta$ is the angle, $m$ is the order number, and $\lambda$ is the wavelength. For the first-order maximum ($m = 1$), rearranging gives $d = \frac{\lambda}{\sin \theta}$. Substituting $\lambda = 589 \, \text{nm}$ and $\theta = 40.0^\circ$, we find $d \approx 916 \, \text{nm}$.

What Slit Separation Would a Grating Have to Produce a First-Order