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Консультация № 160318
12.02.2009, 19:54
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Здравствуйте дорогие эксперты, помогите решить задачку:
На щель шириной 0,3 мм падает нормально параллельный пучок монохроматического света с длиной волны 0,45 мкм. Найти ширину центрального дифракционного максимума на экране, удаленном от щели на 1 м.
На щель шириной 0,3 мм падает нормально параллельный пучок монохроматического света с длиной волны 0,45 мкм. Найти ширину центрального дифракционного максимума на экране, удаленном от щели на 1 м.
Обсуждение
Неизвестный
13.02.2009, 13:45
общий
это ответ
Здравствуйте, Мария Романова!
Решение:
Дано: а = 0,3мм = 0,3*10^-3м; λ = 0,45мкм = 0,45*10^-6м; L = 1м.
Центральный максимум интенсивности света занимает область между ближайшими от него справа и слева минимумами интенсивности. Поэтому ширину центрального максимума интенсивности примем равной расстоянию между этими двумя минимумами.
Минимумы интенсивности света при дифракции от одной щели наблюдаются под углами φ, оп-ределяемыми условием: а*sinφ = ±k*λ, (1)
где k – порядок минимума, равный для нашего случая единице.
Расстояние между двумя минимумами (из геометрических построений): l = 2*L*tg φ.
При малых углах tg φ ≈ sin φ, поэтому можно записать l = 2*L*sin φ. (2)
Найдем sin φ из формулы (1) и подставим его в равенство (2): l = 2*L*k*λ/a.
Произведем вычисления: l = 2*1м*1*0,45*10^-6м/0,3*10^-3м = 3*10^-3 м = 3мм.
Ответ: 3мм.
Решение:
Дано: а = 0,3мм = 0,3*10^-3м; λ = 0,45мкм = 0,45*10^-6м; L = 1м.
Центральный максимум интенсивности света занимает область между ближайшими от него справа и слева минимумами интенсивности. Поэтому ширину центрального максимума интенсивности примем равной расстоянию между этими двумя минимумами.
Минимумы интенсивности света при дифракции от одной щели наблюдаются под углами φ, оп-ределяемыми условием: а*sinφ = ±k*λ, (1)
где k – порядок минимума, равный для нашего случая единице.
Расстояние между двумя минимумами (из геометрических построений): l = 2*L*tg φ.
При малых углах tg φ ≈ sin φ, поэтому можно записать l = 2*L*sin φ. (2)
Найдем sin φ из формулы (1) и подставим его в равенство (2): l = 2*L*k*λ/a.
Произведем вычисления: l = 2*1м*1*0,45*10^-6м/0,3*10^-3м = 3*10^-3 м = 3мм.
Ответ: 3мм.
Форма ответа
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