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# Physics as unit2_42_diffraction_grating

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• 1. Book Reference : Pages 205-2071. To understand diffraction gratings2. To understand how changing wavelength and slit size affect the transmitted pattern3. To understand how the diffraction grating equation is derived4. To be able to complete diffraction grating related calculations
• 2. A diffraction grating is plate with many parallelslits in it.
• 3. 1. Light passing through each slit is diffracted2. The Diffracted light wave from adjacent slits interfere, (reinforce each other) in certain directions only
• 4. 1. The central beam is referred to as the “zero order beam”2. The other beams are numbered outwards on each side: 1st order, 2nd order etc
• 5. 1. How does the diffraction pattern change with wavelength?2. How does the diffraction pattern change with slit distance? Virtual Physics Lab : Waves  Diffraction
• 6. 1. How does the diffraction pattern change with wavelength? The angle of diffraction between each beam and the zero order beam increases with increasing wavelength (Blue to Red)2. How does the diffraction pattern change with slit distance? The angle of diffraction between each beam and the zero order beam increases with decreasing gap size
• 7. 1. Each diffracted wavefront reinforces an adjacent wavefront2. Wavefront at P reinforces wavefront at Y one cycle earlier which in turn reinforces wavefront at R one cycle earlier3. This forms a new wavefront PYZ which travels in a certain direction and forms a diffracted beam
• 8. Formation of nth order beam Q Wavefront at P reinforces Y wavefront from Q emitted nd θ cycles earlier. Wavefront from Q has P θ travelled n wavelengths. QY is nλ sin θ = QY/QP (substitute) sin θ = nλ /d (rearrange)Where d is the slit separation,n is the order of the diffracted dsin θ = nλbeam and λ is the wavelength
• 9. Notes The number of slits per metre N is 1/d As d decreases the angle of diffraction increases. (As N increases, the angle of diffraction increases) Maximum number of orders is when θ = 90° and hence sin θ = 1 ∴ n = d/λ (Rounded down to the nearest whole number)
• 10. A laser of wavelength 630nm is directed normallyat a diffraction grating with 300 lines per mm.Calculate : a) The angle of diffraction for the first two orders [10.9° & 22.2°] b) The number of diffracted orders produced [5]
• 11. Light incident normally on a diffraction gratingwith 600 lines per mm contains wavelengths of580nm and 586nm only. a) How many diffracted orders are seen in the transmitted light [2] b) For the highest order calculate the angle between the two diffracted beams [0.58°]
• 12. Light of wavelength 480nm is incident normally ona diffraction grating the 1st order transmittedbeams are at 28° to the zero order beam.Calculate: a) The number of slits per mm for the grating [1092] b) The angle of diffraction for each of the other diffracted orders [69.9°]