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Консультация № 176574
08.02.2010, 20:46
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Парочка задач на тему: Дифракция
Задача №1
Определите разрешающую способность решетки R шириной l = 4 см и периодом d = 2 мкм в спектре первого порядка. Определите максимальную разрешающую Rmax такой решетки и полное число максимумов, образованных в данном случае.
Задача №2
На диафрагму с круглым отверстием диаметром d = 4 мм падает нормально параллельный пучок монохроматического света с длинной волны 500 нм. Точка наблюдения находится на оси отверстия на расстоянии b = 1 м от него. Сколько зон Френеля укладывается в отверстии? Темное или светлое пятно получится в центре дифракционной картины, если в месте наблюдения поместить экран?
Задача №1
Определите разрешающую способность решетки R шириной l = 4 см и периодом d = 2 мкм в спектре первого порядка. Определите максимальную разрешающую Rmax такой решетки и полное число максимумов, образованных в данном случае.
Задача №2
На диафрагму с круглым отверстием диаметром d = 4 мм падает нормально параллельный пучок монохроматического света с длинной волны 500 нм. Точка наблюдения находится на оси отверстия на расстоянии b = 1 м от него. Сколько зон Френеля укладывается в отверстии? Темное или светлое пятно получится в центре дифракционной картины, если в месте наблюдения поместить экран?
Обсуждение
13.02.2010, 09:28
общий
это ответ
Здравствуйте, Шалимов Александр Сергеевич.
2. Выполним рисунок.
Кратко излагаем решение задачи. Из рисунка видно, что
r2 + b2 = (b + mλ/2)2, r2 = bmλ + m2λ2/4, и при λ << b r = √(bmλ), m = r2/(bλ).
При r = 4/2 = 2 (мм) = 2 ∙ 10-3 м, b = 1 м, λ = 500 нм = 500 ∙ 10-9 м получаем
m = (2 ∙ 10-3)2/(1 ∙ 500 ∙ 10-9) = 8 – число зон Френеля.
Поскольку m – четное, то в центре дифракционной картины будет наблюдаться минимум.
С уважением.
2. Выполним рисунок.
Кратко излагаем решение задачи. Из рисунка видно, что
r2 + b2 = (b + mλ/2)2, r2 = bmλ + m2λ2/4, и при λ << b r = √(bmλ), m = r2/(bλ).
При r = 4/2 = 2 (мм) = 2 ∙ 10-3 м, b = 1 м, λ = 500 нм = 500 ∙ 10-9 м получаем
m = (2 ∙ 10-3)2/(1 ∙ 500 ∙ 10-9) = 8 – число зон Френеля.
Поскольку m – четное, то в центре дифракционной картины будет наблюдаться минимум.
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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