A diffraction grating has 500 slits/mm. What is the longest wavelength of light for which there will be a third-order maximum?

The longest wavelength of light is 666.7 nm

Explanation:

The general form of the grating equation is

mλ = d (sinθi + sinθr)

where;

m is third-order maximum = 3

λ is the wavelength,

d is the slit spacing (m/slit)

θi is the incident angle

θr is the diffracted angle

Note: at longest wavelength, sinθi + sinθr = 1

λ = d/m

d = 1/500 slits/mm

λ = 1 mm / (500 * 3) = 1mm/1500 = 666.7 X 10⁻⁶ mm = 666.7 nm

Therefore, the longest wavelength of light is 666.7 nm