diffraction gratings

• if you repeat Young's double slit experiment with more than two equally spaced slits, you get basically the same pattern as for two slits, but the bands are brighter and narrower and the dark areas are darker.
• when monochromatic light is passed through a grating with hundreds of slits per millimetre, the interference pattern is really sharp because there are so many beams reinforcing the pattern. these sharp fringes make for more accurate measurements
• for monochromatic light on a diffraction grating, there is a line of maximum brightness at the centre called the zero order line. the lines either side of the central one are called first order lines.
• for diffraction gratings:

  $d\sin\theta=$$n\lambda$

  • $d$ = slit separation
  • $\theta$ = angle between incident beam and nth order maximum
  • $\lambda$ = wavelength
• for diffraction gratings:

  • if wavelength is bigger,$sin\theta$ is bigger, so$\theta$ is bigger. this means that the larger the wavelength, the more the pattern will spread out
  • if d (slit separation) is bigger, $sin\theta$ is smaller. this means that the coarser the grating, the less the pattern will spread out
  • values of $sin\theta$ greater than 1 are impossible. so if for a certain value of n, you get a result of more than 1 for $sin\theta$, you know that order doesn't exist
• when using diffraction gratings with white light, each order in the pattern becomes a spectrum, with red on the outside and violet on the inside. the zero order maximum stays white as all the wavelengths pass straight through.
• astronomers and chemists often need to study spectra to help identify elements.

  the wavelength of xrays is of similar scale to the spacing between atoms in crystalline solids, meaning xrays form a diffraction pattern when directed at thin cyrstal. the spacing between the atoms can therefore be found from the diffraction pattern. this is called xray crystallography.