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PHYSHW10 - Thefi pmdnced by a diffractinn grating If we...

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Unformatted text preview: Thefigureshnwsaredlineandagreenlinscfthesarnenrderinthspattern pmdnced by a diffractinn grating. If we increased the grating spacing... (a) Wenld the separatinn cf the lines increase. decrease. er remain the same? (b) Wculd the litres shift tn the right, tc lire left. cr remain in the same place? Snluticn: Increasing the grating spacing means increasing the value If that appears in the grating equatinn dsinfl=nL3L Fer each line. since the nrder [m] isn't changing. and the wavelength cf the spectral line is the same. the right—hand side cf the equaticn remains ccnstant. This implies that sin 15' has tn decrease {sc Hdecreases} tc ccmpensate fer the increase in d This has twc cnnsequences: {aJLet's cnnsider the separatinn between the twn lines. Per the twc wavelengths, we can write dfiiflfll =71»?1 and dsmflg=mfiw which we can combine intn disillGI-BinflzerM-lfl- Again, the right—hand side cf this equatic-n stays crmstant, sc- increasing d means that the difference in sines has tn decrease. This implies that the difference in angles decreases. sn that the line spacing decreases. {hj'Ihe angular p-nsitinn cf each line decreases. sn that means that the line meves clcser tn the center cf the screen. Which way is the center“;I Well, cur grating equaticn aisc tells us that shcrter wavelengths imply smaller angles. which means the green line is clcser tn the center titan the red line. Put tcgether. this means the litres shift tn the right cf the diagram ...
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