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Консультация № 171175
09.08.2009, 11:29
0.00 руб.
0
1
1
Здравствуйте уважаемые эксперты, помогите пожалуйста решить задачу:
На дифракционную решетку в направлении нормали к ее поверхности падает монохроматический свет. Период решетки d = 2 мкм. Какого наибольшего порядка главный максимум дает эта решетка в случае красного света ([$955$]1 = 0.7 мкм) и в случае фиолетового ([$955$]2 = 0.45 мкм)?
На дифракционную решетку в направлении нормали к ее поверхности падает монохроматический свет. Период решетки d = 2 мкм. Какого наибольшего порядка главный максимум дает эта решетка в случае красного света ([$955$]1 = 0.7 мкм) и в случае фиолетового ([$955$]2 = 0.45 мкм)?
Обсуждение
09.08.2009, 20:55
общий
это ответ
Здравствуйте, Чаркин Иван Александрович.
Если не ошибаюсь, ход решения следующий.
Для того, чтобы в точке за решеткой наблюдался интерференционный максимум порядка m, разность хода ∆ между волнами, испущенными соседними щелями дифракционной решетки, должна быть равна целому числу длин волн, т. е. должно выполняться условие
∆ = d ∙ sin φm = mλ, (1)
где m – целое число, φ – угол дифракции.
Максимальный порядок спектра будет при sin φm = 1. Следовательно, из формулы (1),
mmax ≤ d/λ. (2)
Подставляем в формулу (2) числовые значения величин и получаем:
- для красного света
mmax ≤ d/λ1 = 2/0,7 ≈ 2,9, тогда mmax = 2 (ближайшее целое число, меньшее, чем 2,9);
- для фиолетового света
mmax ≤ d/λ2 = 2/0,45 ≈ 4,4, тогда mmax = 4 (ближайшее целое число, меньшее, чем 4,4).
Ответ: 2; 4.
С уважением.
Если не ошибаюсь, ход решения следующий.
Для того, чтобы в точке за решеткой наблюдался интерференционный максимум порядка m, разность хода ∆ между волнами, испущенными соседними щелями дифракционной решетки, должна быть равна целому числу длин волн, т. е. должно выполняться условие
∆ = d ∙ sin φm = mλ, (1)
где m – целое число, φ – угол дифракции.
Максимальный порядок спектра будет при sin φm = 1. Следовательно, из формулы (1),
mmax ≤ d/λ. (2)
Подставляем в формулу (2) числовые значения величин и получаем:
- для красного света
mmax ≤ d/λ1 = 2/0,7 ≈ 2,9, тогда mmax = 2 (ближайшее целое число, меньшее, чем 2,9);
- для фиолетового света
mmax ≤ d/λ2 = 2/0,45 ≈ 4,4, тогда mmax = 4 (ближайшее целое число, меньшее, чем 4,4).
Ответ: 2; 4.
С уважением.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
Форма ответа
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