presentsa production Diffraction 1 Background Image: PHET
Simple diffraction Wave energy spreading out when it passes anedge or an aperture (aperture is really two edges) "no-one has ever been able to deﬁne the difference between interference and diffraction satisfactorily. It is just a question of usage, and there is no speciﬁc, important physical difference between them." Richard Feynman
Changing wavelength Diffraction is greater if the wavelength is longer. At the edge, some wave energy is diffracted obstacle (spreads into the shadow of the obstacle). More energy spreads out if the wavelength is longer. obstacle Images: Kiselev
Changing aperture Aperture = hole = gap = slit = two edges There is greater diffraction when the wave passes through a narrow aperture. Images: PHET
More diffraction The amount of diffraction depends on boththe wavelength and the width of the aperture. It depends on the ratio of wavelength/ aperture width Diffraction is greatest if the wavelength is large compared with the aperture.
Diffraction pattern When the Central maximum First minimum aperture is larger, it Second minimum behaves not Wave intensity graph like a single source, butlike a number Pattern on screen of sources spread across the aperture. Incident wavefronts Image: Kiselev
Light through a slit Changing slit width, constant wavelength A narrower slit (aperture) causes the wave energy to spread out more. A wider slit causes the diffraction maxima to be closerImages: Kiselev together.
Light through a slitChanging wavelength, constant slit widthA shorter wavelengthcauses the energy to spread out less.A longer wavelengthcauses the diffraction maxima to be wider apart Images: Kiselev
Path differencesImage: PHET Central max path diff = 0 The path difference is how much further the wave from the top half of the slit has travelled than the wave from the bottom. First max First minpath diff = one wavelength path diff = half wavelength
Diffraction formulaThe path difference for the The waves from the topﬁrst minimum is half a and bottom halves of thewavelength. AB is the slit of slit interfere destructivelywidth b. at a distant screen. We can A assume the rays are parallel since the screen is far away. 90˚b b/2 B
Diffraction geometry The angular position of the diffraction Units minimum is proportional to the wavelength Angles and inversely proportional to the slit width. in rads; Lengths in any x unit so D long as they are theD = screen distance same inx = position of ﬁrst min. (or half-width central max.) each formula.
Diffraction practice We can calculate the angular position of the minimum using the distance of the screen from the slit, the distance of the minimumfrom the centre of the pattern and the small angle approximation. A laser is diffracted at a slit of width 0.20 mm. It forms a pattern 2.2 m away. The ﬁrst minimum is 6.5 mm from the centre of the pattern. What is the wavelength of the light? [590 nm] If a slit diffracts 650 nm light so that the diffraction maximum is 4.0 cm wide on a screen, what will be the width of the diffraction maximum for light of wavelength 420 nm? [2.6 cm]
Diffraction examples The regular surface of a CD diffracts different wavelengths of light at different angles and produces a spectrum. Diffraction pattern of a square aperture is 2-dimensional. Photo of X-ray diffraction pattern of DNA taken by Rosalind Franklin and interpreted by Crick and Watson.Image: sciencephoto.com
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