diffraction grating has 5150 lines per centimeter ruled on it. What is the angular separation between the first - and the third-order bright spots on the same side of the central maximum when the grating is illuminated by a beam of light with wavelength 633 nm

width of slits a = 1 x 10⁻² / 5150

= 1.941 x 10⁻⁶ m

angular position of first bright fringe = λ / a, λ is wavelength of light

= 633 x 10⁻⁹ / 1.941 x 10⁻⁶

= 326.12 x 10⁻³ radian

angular position of third bright fringe = 3 λ / a, λ is wavelength of light

= (3 x 633 x 10⁻⁹) / 1.941 x 10⁻⁶

= 978.36 x 10⁻³ radian

angular separation between the two

= 978.36 x 10⁻³ - 326.12 x 10⁻³

= 652.24 x 10⁻³ radian.