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Здравствуйте, уважаемые эксперты! Помогите, пожалуйста, решить следующие задачи по физике:
1. На какое расстояние "дельта"h в установке, описанной в задаче 23 (ссылки ниже), следует отодвинуть от зеркала источник света, чтобы на месте кольца с номером k оказалось кольцо с номером на единицу больше? Расстояние k от источника света до зеркала считать известным. Использовать условие малости углов Q.
В условии одной и той же буквой k обозначены две разные величины: номер кольца и расстояние от источника света до зеркала, что недопустимо. Можно ли считать, что в условии опечатка, и расстояние от источника света до зеркала обозначается буквой h? И надо ли решать саму задачу 23, т.е. "Получить выражение для радиусов тёмных колец", или можно считать, что оно уже известно?
Неизвестный
18.12.2013, 11:31
общий
Адресаты:
Это я неправильно написал, виноват "Расстояние h от источника света до зеркала считать известным. Использовать условие малости углов Q."
Здравствуйте, Барс Иван! 1. Источник света и его отражение в зеркале находятся на расстоянии 2h друг от друга. При h достаточно малом по отношению к l разность расстояний до источника и отражения от точки, радиус-вектор к которой составляет угол [$629$] с перпендикуляром к зеркалу, составляет 2h[$183$]cos[$629$] Учитывая потерю полуволны при отражении, общая разность хода составляет [$916$]x=2h[$183$]cos[$629$]+[$955$]/2 условие минимума (тёмного кольца) [$916$]x=k[$955$]+[$955$]/2 2h[$183$]cos[$629$]+[$955$]/2=k[$955$]+[$955$]/2 2h[$183$]cos[$629$]=k[$955$] Условие смещения на одно кольцо: 2(h+[$916$]h)[$183$]cos[$629$]=(k+1)[$955$] 2[$916$]h[$183$]cos[$629$]=[$955$] Для малых углов косинус близок к 1 и поэтому [$916$]h=[$955$]/2
Для произвольного k можно выразить косинус угла cos[$629$]=k[$955$]/2h Тогда смещение [$916$]h=[$955$]/2cos[$629$]=h/k (учтите, что у центрального минимума/максимума самое большое значение k, а k=0 соответствует направление, параллельное плоскости зеркала) Также отметим, что нахождения собственно радиусов колец на экране для решения задачи не требуется.
2. Для качественного описания дифракции на одной щели достаточно найти разность хода лучей, идущих через края щели. Клин усложняет ситуацию, давая некую разность фаз между краями щели. Найдём её: Рассмотрим некий срез плоскостью перпендикулярной поверхностям клина. Пусть A - точка на краю щели, ближайшем к ребру клина, а B - точка на удалённом от ребра клина краю. Тогда свет идущий в точку B должен пройти дополнительно расстояние b[$183$]sin[$966$] в среде с коэффициентом n, что соответствует разности хода [$916$]xB=bn[$183$]sin[$966$] поскольку сведений про экран нам не дано, найдём угловую ширину линий. За нулевое направление примем нормаль к непрозрачной стороне клина, пусть положительные углы [$945$] соответствуют отклонению к ребру клина, а отрицательные - от ребра. В этом случае разность расстояний от некой точки C, находящейся на большом расстоянии от щели на прямой составляющей с нормалью к щели угол [$945$], равна BC-AC=b[$183$]sin[$945$] добавляем к этому разность хода на самой щели и получаем разность хода [$916$]x=b[$183$]sin[$945$]+bn[$183$]sin[$966$]
Далее возникает сложность с определением "ширина максимума". Могу предложит 3 варианта определения его краёв: а) разность хода [$916$]x=[$177$][$955$]/2 - собственно та отметка, на которой впервые появляются волны противоположных фаз, гасящие друг друга. Кстати, это условие соответствует выражению для всех максимумов кроме нулевого. б) разность хода [$916$]x=[$177$][$955$] - первый минимум в) разность хода [$916$]x=[$177$]3[$955$]/4 - посередине между предыдущими двумя вариантами.
Кстати, какое в Вашем задачнике значение n для стекла? А то у него в зависимости от состава оно может принимать очень разные значения.
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