A diffraction grating has 450 lines per millimeter. What is the highest order $m$ that contains the entire visible spectrum from $400 \mathrm {~nm}$ to $700 \mathrm {~nm}$ ?
A) $m = 2$
B) $m = 3$
C) $m = 5$
D) $m = 4$
E) $m = 6$

Question

Quizplus · Accepted Answer

The highest order $m$ is determined by the grating equation $d \sin \theta = m \lambda$, where $d$ is the distance between lines. For 450 lines/mm, $d = \frac{1}{450,000} \, \text{m}$. The maximum $m$ occurs when $\sin \theta = 1$. Using $\lambda = 700 \, \text{nm}$, $m = \frac{d}{\lambda} = \frac{1}{450,000 \times 700 \times 10^{-9}}$, which gives $m \approx 3.17$. Thus, the highest integer $m$ is 3.

A Diffraction Grating Has 450 Lines Per Millimeter mmm That Contains the Entire Visible Spectrum From

A Diffraction Grating Has 450 Lines Per Millimeter $m$ That Contains the Entire Visible Spectrum From