The Diffraction Grating

1. The Diffraction Grating

2. 600mm-1 • A (transmission) diffraction grating is an arrangement of identical, equally spaced parallel lines ruled on glass. • A typical diffraction grating will have something like.600 lines per millimetre Diffraction gratings are used to produce optical spectra

3. Light of wavelength λ, normal to the grating Each of the clear spaces (A,B,C etc) acts like a very narrow slit and produces its own diffraction. The light is from the same monochromatic source and therefore is coherent. A d B θ C

4. θ θ Light of wavelength λ, normal to the grating Consider the light which is diffracted by each slit at some angle θ to the normal. A θ d B The slits are equally spaced so that if angle θ produces light that phase at A and B (and therefore positively reinforces ) then the light will also be in phase from every other slit and also produce positive reinforcement. C

5. θ θ Light of wavelength λ, normal to the grating When the waves reinforce each other the path difference AN is a full number of wavelengths . A θ N d That means that AN =nλ where n is a whole number B As: AN = d sin θ C dsinθ = nλ

6. Diffraction Grating • The angle θ will be slightly different for each wavelength of light and so the grating separates white light into its spectrum and does this much more effectively than a prism. • The light needs to be focussed with the eyepiece lens of a telescope or spectrometer ( or the lens of the eye) after it emerges from the grating.

7. The Diffraction Grating • A diffraction grating with a large number of lines produces very sharp maxima and completely destructive interference at other angles

8. Calculations • A diffraction grating has 600 lines per mm. If such a grating is illuminated with yellow light at 6 x 10-7 m, calculate the angle at which zero, first and second order diffraction will be observed The diagram below shows the light passing through the grating. zero order diffraction is always at 00 to the normal! zero order diffraction first order diffraction grating second order diffraction

9. zero order diffraction first order diffraction grating second order diffraction Calculations The spacing of the lines(d) is 1/600 000 mm • A diffraction grating has 600 lines per mm. If such a grating is illuminated with yellow light at 6 x 10-7 m, calculate the angle at which zero, first and second order diffraction will be observed Using nλ= dsinθ 21.10

10. zero order diffraction first order diffraction grating second order diffraction Calculations The spacing of the lines(d) is 1/600 000 mm • A diffraction grating has 600 lines per mm. If such a grating is illuminated with yellow light at 6 x 10-7 m, calculate the angle at which zero, first and second order diffraction will be observed Using nλ=dsinθ 21.10 Try to calculate the angle for 3rd order diffraction

11. Calculations When a grating with 300 lines per mm is illuminated normally with a parallel beam of monochromatic light a second order principle maximum is observed at 18.90 to the straight through direction. Find the wavelength of the light 300 lines per mm is 3.00 x 105 lines per metre and therefore the spacing d =1/3.00 x 105m A second order maximum means n=2 Using nλ= dsinθ