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INTERFERENCE Interference patterns are a direct result of superpositioning. Antinodal and nodal lines are produced. These patterns can be enhanced using diffraction gratings, where all waves pass through each other from multiple point sources. We also learnt that the path difference for a point on a an antinodal line is always a factor of a wavelength, , whereas for a nodal line is half a wavelength, ½. Antinodal line path difference = n Nodal line path difference = n½ Where n = order 0, 1, 2, 3, ……. Red: crest meets crest Or trough meets trough. Constructive interference Blue: crest meets a trough and they cancel out. Destructive interference Can be used to calculate the path difference. Whole numbers: antinodal lines Half numbers: nodal lines 5 wavelengths 6 wavelength s S1 and S2 are two coherent sources All points on a wavefront are in phase with one another Waves interfere constructively where wavefronts meet. = antinodal lines 2 1 Along the nodal lines, destructive interference occurs. Here antiphase wavefronts S2 meet. 0 1 2 Wave Intensity (Fringes) n = order number S1 Young’s Double Slits A series of dark and bright fringes on the screen. Monochromatic light, wavelength Double slit Screen Young’s Double Slit Experiment THIS RELIES INITIALLY ON LIGHT DIFFRACTING THROUGH EACH SLIT. Where the diffracted light overlaps, interference occurs Light INTERFERENCE Double slit Diffraction screen Some fringes may be missing where there is a minimum in the diffraction pattern Assuming the sources are coherent Wave trains AP & BP have travelled the same distance (same number of ’s) A P B Hence waves arrive in-phase CONSTRUCTIVE INTERFERENCE (Bright fringe) Slits d L d = slit separation dx n L Screen x = fringe separation Normal light sources emit photons at random, so they are not coherent. LASER LASERS EMIT COHERENT LIGHT LASER Example 5: Monochromatic light from a point source illuminates two parallel, narrow slits. The centres of the slit openings are 0.80mm apart. An interference pattern forms on screen placed 2.0m away. The distance between two adjacent dark fringes is 1.2mm. Calculate the wavelength, , of the light used. Example 5: Monochromatic light from a point source illuminates two parallel, narrow slits. The centres of the slit openings are 0.80mm apart. An interference pattern forms on screen placed 2.0m away. The distance between two adjacent dark fringes is 1.2mm. Calculate the wavelength, , of the light used. SOLUTION: The distance to the screen (2.0m) is large compared with the fringe spacing (1.2mm). The approximation formula can be used. n = dx/L [n = 1 because the fringe spacing is being calculated] = (8.0 x 10-4 x 1.2 x 10-3) / 2.0 = 4.8 x 10-7 m Decide which points are Constructive interference and which are Destructive interference? In phase Out of phase By 180 deg (half a wavelength) Quantum Physics. http://www.doubleslitexperiment.com/ Double slit animation. http://www.colorado.edu/physics/2000/schro edinger/two-slit2.html dx n L PD= m λ Two point sources, 3.0 cm apart, are generating periodic waves in phase. A point on the third antinodal line of the wave pattern is 10 cm from one source and 8.0 cm from the other source. Determine the wavelength of the waves. Two point sources are generating periodic waves in phase. The wavelength of the waves is 3.0 cm. A point on a nodal line is 25 cm from one source and 20.5 cm from the other source. Determine the nodal line number. The Diffraction Grating: This is a piece of glass with tiny slits made in it to produce small point sources. A formula can be used to relate to the interference pattern produced by a particular diffraction grating. dsin = n (Where n = 0, 1, 2, 3 …….) Often N, the number of slits per metre, or slits per centimetre is given. The slit spacing d is related to N by: d = 1/N A C Monochromatic light B Grating 1 d number of lines per metre d sin n red light 700 nm, violet light 400 nm Several spectra will be seen, the number depending upon the value of d Second Order maximum, n = 2 First Order maximum, n = 1 White Central maximum, n = 0 First Order maximum, n = 1 Grating Second Order maximum, n = 2 screen n=3 n=2 n=1 n=0 Note that higher orders, as with 2 and 3 here, can overlap Note that in the spectrum produced by a prism, it is the blue light which is most deviated grating Example: Light from a laser passes through a diffraction grating of 2000 lines per cm. The diagram below shows the measurement made. 0 order laser 0.5m Grating 2m 2nd order Calculate the wavelength of the light. SOLUTION: sin = 0.5/2 Slit spacing d = 1/N = 1/200000 = 0.250 = 5.00 x 10-6m = dsin/n = (5.00 x 10-6 x 0.250) / 2 = 6.25 x 10-7m http://webphysics.ph.msstate.edu/javamirror /ipmj/java/slitdiffr/index.html