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Консультация № 137915
26.05.2008, 21:50
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Определить длну волны спектральной линии, изображение которой, даваемое дифракционной решеткой в спектре третьего порядка, совпадает с изображением линии с lambda = 4861 Ангстрем в спектре четвертого порядка.
Обсуждение
Неизвестный
28.05.2008, 09:26
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это ответ
Здравствуйте, Сергей Викторович Арефин!
Уравнение дифракции на дифракционной решетке выглядит как:
d*sin(fi)=m*λ (1)
где d - постоянная решетки, m - порядок спектра, λ - длина волны света; fi - угол отклонения дифрагированного луча от его первоначального направления
Если две спектральные линии совпадают, значит они наблюдаются под одним углом fi, а значит, левые части уравнения (1) для них одинаковы; отличаются же порядки и длины волн, т.е. для первой линии имеем:
d*sin(fi)=m<sub>1</sub>*λ<sub>1</sub> (2)
где m<sub>1</sub>=3, λ<sub>1</sub> - искомая длина волны; для второй линии:
d*sin(fi)=m<sub>2</sub>*λ<sub>2</sub> (3)
где m<sub>2</sub>=4, λ<sub>2</sub>=4861 Ангстрем.
Приравнивая правые части (2) и (3) выражаем λ<sub>1</sub>:
λ<sub>1</sub>=m<sub>2</sub>*λ<sub>2</sub>/m<sub>1</sub>=4*4861/3=6481 Ангстрем
Уравнение дифракции на дифракционной решетке выглядит как:
d*sin(fi)=m*λ (1)
где d - постоянная решетки, m - порядок спектра, λ - длина волны света; fi - угол отклонения дифрагированного луча от его первоначального направления
Если две спектральные линии совпадают, значит они наблюдаются под одним углом fi, а значит, левые части уравнения (1) для них одинаковы; отличаются же порядки и длины волн, т.е. для первой линии имеем:
d*sin(fi)=m<sub>1</sub>*λ<sub>1</sub> (2)
где m<sub>1</sub>=3, λ<sub>1</sub> - искомая длина волны; для второй линии:
d*sin(fi)=m<sub>2</sub>*λ<sub>2</sub> (3)
где m<sub>2</sub>=4, λ<sub>2</sub>=4861 Ангстрем.
Приравнивая правые части (2) и (3) выражаем λ<sub>1</sub>:
λ<sub>1</sub>=m<sub>2</sub>*λ<sub>2</sub>/m<sub>1</sub>=4*4861/3=6481 Ангстрем
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