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Консультация № 202415

22.03.2022, 19:02

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Образование

Здравствуйте! Прошу помощи в следующем вопросе:
При наблюдении дифракционной картины, даваемой дифракционной решёткой при нормальном падении на неё света, два соседних максимума одной и той же спектральной линии наблюдают под углами фи_k=14,5 градусов и фи_(k+1)=20,5 градусов; постоянная решётки, длина волны света и порядки дифракции k и k+1 не известны. Чему равен угол дифракции той же линии в первом порядке?

Обсуждение

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Посетитель
226425
1567

26.03.2022, 01:25

общий

26.03.2022, 01:26

это ответ

Здравствуйте, marigrineva
Дано:
[$966$]_k=14,5[$176$]
[$966$]_k+1=20,5[$176$]
Найти: [$966$]₁
Решение:
Формула дифракционной решетки
d*sin[$966$]=k*[$955$] (*),
где
d - период (постоянная) решетки;
[$955$] - длина световой волны;
k - порядок максимума (целое число (k[$8712$]Z)).
Тогда
d=k*[$955$]/sin[$966$]_k=(k+1)*[$955$]/sin[$966$]_k+1
Отсюда
(k+1)/k=sin[$966$]_k+1/sin[$966$]_k[$8776$]0,350/0,250[$8776$]1,4
Методом подбора получаем
k=3
((3+1)/3[$8776$]1,33[$8776$]1,4)
Из формулы (*) следует:
[$955$]/d=sin[$966$]_k/k=0,250/3[$8776$]0,0833
или
[$955$]/d=sin[$966$]_k+1/(k+1)=0,350/4[$8776$]0,0875
тогда среднее значение
[$955$]/d=(0,0833+0,0875)/2[$8776$]0,085
Тогда
при k=1
[$955$]/d=sin[$966$]₁/1
Следовательно
[$966$]₁=arcsin([$955$]/d)=arcsin0,085[$8776$]4,9[$176$]
*******
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Об авторе:
С уважением
shvetski

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12

26.03.2022, 09:05

общий

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Здравствуйте, спасибо за решение

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