9.4 Resolution

THE IB SAYS

Understandings: The size of a diffracting aperture; The resolution of simple monochromatic two-source systems

Applications and skills: Solving problems involving the Rayleigh criterion for light emitted by two sources diffracted at a single slit; Resolvance of diffraction gratings

Guidance: Proof of the diffraction grating resolvance equation is not required

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Resolution and the Rayleigh Criterion

If you look at, or take a photograph, of the front of a car (with its headlights on) at night you will see two light sources. But if you move away from the car then, eventually, you will only see one. The distance at which this happens depends on the resolution of your imaging system. These systems have two components: the optics and the sensor. Ignoring the sensor for now, the maximum possible resolution of the optics is determined by the Rayleigh Criterion. This states that two point sources of light are resolvable if the maximum of one lies on the first minimum of the other (see diagram above). This angle in turn is directly proportional to the wavelength of the light, and inversely proportional to the diameter of the aperture. Thus cameras and telescopes with large aperture lenses are better at resolving visible light.

Resolvance

The resolvance of a diffraction grating is a measure of how good it is at producing narrow - and therefore easily distinguishable - spectral lines. The smallest difference that can be distinguished is labelled ∆λ and resolvance is defined as the ratio of the observed wavelength to that smallest difference, such that R = λ/ ∆λ. The resolvance for a particular diffraction grating is R = Nm where N is the number of slits illuminated by the beam and m is the diffraction order. Using higher orders will improve R, but there is a limit to how high you can go and higher orders are fainter. Therefore increasing N is better option, and the best way to do this is by increasing the number of slits per mm your chosen diffraction grating has.

Resources from textbooks

Oxford Physics: pages 376 - 380, includes worked examples on page 378 and page 380

Hamper HL (2014): pages 191 - 192 cover resolution and the Rayleigh criteria, pages 195- 197 cover resolvance (as part of a look at diffraction gratings)

Relevant questions from Dot Point Physics (11. Wave phenomena)

Oscillations and waves, pages 103 - 106

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