Question

If the distance between slits on a diffraction grating is 0.50 mm and one of the angles of diffraction is 0.25°, how large is the path difference?

Answer 1

The path difference between two waves is the distance between the two waves. This distance may be obtained as the product of the order of the maxiuma or minima and the wavelength of the wave. The formula is:
d*sin∅ = nλ

Substituting the values for the distance between slits and the angle:
nλ = 0.05 * sin(0.25)
nλ = 2.18 x 10⁻⁴ m

The path difference is 0.2 millimeters.

Answer 2

It should be 2200 nm and for the second part "How many orders of bright lines does this equal for red light with a wavelength of 650 nm?" it should be 3 wavelengths.