Resolution and Diffraction Gratings

Diffraction "blurs" images together, and places a limit on the finest details one may distinguish
If one looks at two objects through a rectangular slit using light of wavelength lambda, then the two objects will appear to blur together when their projected angular separation is
```
                               lambda
              sin (theta) =  -------------
                             width of slit
```
A similar formula describes the smallest angular separation at which two point sources of light (like headlights, or stars) may be distinguished when one looks through a circular aperture:
```
                                        lambda
              sin (theta) = 1.22  -------------------
                                  diameter of aperture
```
One can increase one's ability to distinguish fine detail by increasing the aperture through which one is looking, or by using light of shorter wavelengths.
A diffraction grating is a device with many, many parallel slits very close together. When light passes through a diffraction grating, it is dispersed into a spectrum.

Light of wavelength lambda which passes through a diffraction grating of spacing d will create a bright spot at angles

                                  lambda
                  sin(theta) =  N ------          for N = 0, 1, 2, 3, ....
                                    d

A diffraction grating disperses light into a rainbow, like a prism; but the order of the colors is opposite for the two devices. A prism throws blue light most away from the center; a grating throws red light most away from the center.
One can use diffraction gratings to stretch light into spectra, then identify different chemical elements and compounds from the patterns of light in the spectra.

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Painter Georges Seurat knew the resolution limit of the human eye and the distance at which spectators typically viewed his work. He used tiny little dots of paint which are just at the limit of resolution to create "A Sunday on La Grande Jatte".

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