A diffraction grating is a slide with many equally spaced parallel slits (lines), often hundreds per millimetre. Light passing through the slits diffracts, and the waves from the slits interfere. Bright maxima (orders) are produced in directions where the waves from neighbouring slits arrive in phase, which happens when the path difference is a whole number of wavelengths:d sin θ = nλ where d is the grating spacing (distance between adjacent slits), θ is the angle of the nth order maximum from the straight-through (zero order) direction, n is the order number and λ is the wavelength. If a grating has N lines per metre, d = 1/N.
Because θ depends on λ, a grating spreads starlight into a spectrum, with red light (longer wavelength) diffracted through larger angles than violet. Gratings give sharp, bright, widely spaced maxima, so the wavelengths of the absorption lines in a star's spectrum can be measured accurately and matched to elements.Worked example: a grating has 500 lines per mm. At what angle is the first order maximum for a hydrogen line of wavelength 656 nm?
d = 1/(500 × 103) = 2.00 × 10−6 m
sin θ = nλ/d = (1 × 656 × 10−9) / 2.00 × 10−6 = 0.328
θ = 19.1°The highest order that can be observed is found from sin θ < 1, so n < d/λ.
Because θ depends on λ, a grating spreads starlight into a spectrum, with red light (longer wavelength) diffracted through larger angles than violet. Gratings give sharp, bright, widely spaced maxima, so the wavelengths of the absorption lines in a star's spectrum can be measured accurately and matched to elements.Worked example: a grating has 500 lines per mm. At what angle is the first order maximum for a hydrogen line of wavelength 656 nm?d = 1/(500 × 103) = 2.00 × 10−6 m
sin θ = nλ/d = (1 × 656 × 10−9) / 2.00 × 10−6 = 0.328
θ = 19.1°The highest order that can be observed is found from sin θ < 1, so n < d/λ.