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Консультация № 138440
29.05.2008, 09:45
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Доброго времени суток! Уважаемые эксперты, помогите пожалуйста решить –
На дифракционную решетку падает нормально параллельный пучок белого света. Спектры третьего и четвертого порядка частично накладываются друг на друга. На какую длину волны в спектре четвертого порядка накладывается граница ( λ = 780 нм ) спектра третьего порядка?
На дифракционную решетку падает нормально параллельный пучок белого света. Спектры третьего и четвертого порядка частично накладываются друг на друга. На какую длину волны в спектре четвертого порядка накладывается граница ( λ = 780 нм ) спектра третьего порядка?
Обсуждение
Неизвестный
29.05.2008, 14:46
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это ответ
Здравствуйте, Петров Василий Алибабаевич!
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 накладываются, 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>=4, 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>=3, λ<sub>2</sub>=780 нм.
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>=3*780/4=585 нм
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 накладываются, 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>=4, 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>=3, λ<sub>2</sub>=780 нм.
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>=3*780/4=585 нм
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