Answer
7140 slits/cm.
Work Step by Step
Solve Eq. 24–4 for the slit separation d.
$$d sin \theta = m \lambda $$
$$d = \frac{m \lambda}{ sin \theta }$$
See Figure 24–26. The angle of the diffracted light increases as the wavelength increases. To be able to view a full order, the largest wavelength in the visible spectrum, 700 nm, must be visible at the maximum angle of diffraction, which is 90 degrees.
Use the largest wavelength with that angle to find the minimum slit separation.
$$d = \frac{2(700\times10^{-9}m)}{sin 90^{\circ}} = 1.40\times10^{-6}m=1.40\times10^{-4}cm $$
The reciprocal of the minimum slit separation gives the maximum number of slits per cm.
$$\frac{1}{d}=\frac{1}{1.40\times10^{-4}cm }=7140\frac{slits}{cm}$$
The answer is reported to 3 significant figures.
