IB Physics Resolution flippingphysics by Nothingnerdy
presentsa production Resolution 1
Circular apertureLight diffracted by a circular aperture forms a pattern of concentric rings with a bright ‘Airy disc’ in thecentre. Examples of circular apertures are the pupil of the eye; a camera lens; a radio telescope dish. Image: livjm.ac.uk
Diffraction patterms Diffraction by circular Diffraction by slit of width b aperture of diameter b Average diameter In both cases, angle is of circle = b/1.22 proportional to wavelength and inversely proportional to slit width.Image: photoresearchers Image: oberlin
Resolution Light passing through an aperture is diffracted. If the images of two objects viewed through the aperture are so close that their diffraction patterns overlap, they will be difﬁcult to resolve. Resolution is the ability to distinguish two separate images. These illuminated objects can be resolved because their Airy discs are separate.Image: NHMFL
Rayleigh criterion Image: NHMFLThe limit of resolvability is when the middle of the central maximum of one image coincides with the ﬁrst minimum of the other. At this limit, the angle subtended by the two points is given by: where b is the diameter of the aperture through which The Rayleigh criterion the objects are viewed.
Better resolution Better resolution means that the angle is as small as possible. This is achieved by using a large aperture or a short wavelength. Thus, big lenses resolve better than small ones and the eye can resolve violet light better than red becausethere is less diffraction at the aperture.
Resolution problemsA light telescope has a circular mirror of radius 127 cm.What is the smallest angle it can resolve for light ofwavelength 550 nm? [264 nrad]Two stars are 20 ly distant and can just be resolved usinga telescope with aperture of 55 cm. How far apart arethe stars? Assume light of wavelength 450 nm.[11.5 light-minutes]Two spotlights are 12 m apart. How far away can ahuman eye (pupil diameter 0.40 cm) distinguish thespotlights if the wavelength of the light is 620 nm?[63 km]
Resolution examplesCDs and DVDs use reﬂection of laser light from ‘pits’ onthe surface. To store more information, the pits must besmaller, but there is a limit to resolvability. One solutionis to use shorter wavelength light.If the object is too small, a light microscope cannotresolve it due to diffraction at the lens; below uv(400nm) the light as not visible. An electron microscopeuses electrons with wavelengths of 0.2 nm.Radio telescopes detect radio waves from space. Sincethese have a long wavelength, and are hard to resolve,the radius of the dishes of the telescopes is huge.
Where these two goldcrystals meet they arejoined by a complexarrangement of atoms,forming a nano-bridge.The atoms are 2.3angstroms apart. This Image from Hubbleresolution is possible Space Telescope ofdue to electron binary star system justmicroscopy. resolved. It is 8 000 ly away and a third unresolved star is suspected.
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