Light with a wavelength of 665 nm is passed through a diffraction grating with 759 slits/cm. Find the angle at which one would observe the first order maximum.

Question

Light with a wavelength of 665 nm is passed through a diffraction grating with 759 slits/cm. Find the angle at which one would observe the first order maximum.

Answer 1

759 slits per centimeter translates to 760 lines per centimeter on the diffraction grating.

Calculate the slit separation (d), which is equal to the inverse of the number of lines per centimeter.

Find d = (1 cm/760 lines) times (10⁷ nm/1 cm) equal to (10⁷nm/760 lines) or 13157.9 nanometers per line.

For the First Order Maximum (m = 1), write sin A_m = mλ/d or sin A₁ = (1)(665 nm)/(13157.9 nm) or 0.05053997978, which gives the angle A₁ as 2.896961712° ≈2.897°.