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Консультация № 189252
23.04.2016, 20:17
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Дифракционная картина наблюдается на расстоянии 4 м от точечного источника монохроматического света (=500 нм). Посредине между экраном и источником света помещена диафрагма с круглым отверстием. При каком ра-диусе отверстия центр дифракционных колец, наблюдаемых на экране, будет наиболее темным?
Дифракционная картина наблюдается на расстоянии 4 м от точечного источника монохроматического света (=500 нм). Посредине между экраном и источником света помещена диафрагма с круглым отверстием. При каком ра-диусе отверстия центр дифракционных колец, наблюдаемых на экране, будет наиболее темным?
Обсуждение
27.04.2016, 01:16
общий
это ответ
Здравствуйте, diam98!
диафрагма находится на расстоянии L1=L2=L/2 как от источника, так и от экрана.
При радиусе отверстия r, лучи идушие от источника к центру и к краю отверстия приобретают разность хода
[$916$][$8467$]1[$8776$]r2L1=2r2/L,
а от этих точек до центра дифракционной картины также возникает разность хода
[$916$][$8467$]2[$8776$]r2L2=2r2/L.
Итого, разность хода [$916$][$8467$]=4r2/L
Наиболее тёмный центр дифракционной картины наблюдается при первом минимуме (2 зоны Френеля), когда разность хода лучей, прошедших через центр и край отверстия, составляет [$916$][$8467$]=[$955$] (при этом в центр дифракционной картины приходят волны всех фаз со сходной амплитудой)
[$955$]=4r2/L
r2=[$955$]L/4
r=[$8730$]([$955$]L/4)=[$8730$](5[$183$]10-7м[$183$]4м/4)=7,07[$183$]10-4 м=0,707 мм
диафрагма находится на расстоянии L1=L2=L/2 как от источника, так и от экрана.
При радиусе отверстия r, лучи идушие от источника к центру и к краю отверстия приобретают разность хода
[$916$][$8467$]1[$8776$]r2L1=2r2/L,
а от этих точек до центра дифракционной картины также возникает разность хода
[$916$][$8467$]2[$8776$]r2L2=2r2/L.
Итого, разность хода [$916$][$8467$]=4r2/L
Наиболее тёмный центр дифракционной картины наблюдается при первом минимуме (2 зоны Френеля), когда разность хода лучей, прошедших через центр и край отверстия, составляет [$916$][$8467$]=[$955$] (при этом в центр дифракционной картины приходят волны всех фаз со сходной амплитудой)
[$955$]=4r2/L
r2=[$955$]L/4
r=[$8730$]([$955$]L/4)=[$8730$](5[$183$]10-7м[$183$]4м/4)=7,07[$183$]10-4 м=0,707 мм
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