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Консультация № 195223
11.04.2019, 23:02
0.00 руб.
0
5
1
Здравствуйте! У меня возникли сложности с этой задачей, помогите пожалуйста:
Период дифракционной решетки равен 7 мкм. Для спектральной линии водорода с длиной волны 486 нм подобрать такой наибольший интервал длин волн, чтобы нигде не было перекрытия спектров при освещении светом в заданном интервале. Ширина дифракционной решетки 3 см. Ответ дать в нанометрах.
Период дифракционной решетки равен 7 мкм. Для спектральной линии водорода с длиной волны 486 нм подобрать такой наибольший интервал длин волн, чтобы нигде не было перекрытия спектров при освещении светом в заданном интервале. Ширина дифракционной решетки 3 см. Ответ дать в нанометрах.
Обсуждение
15.04.2019, 14:28
общий
это ответ
Здравствуйте, ya.anya-semenova!
По формуле дифракционной решётки порядок k спектра и угол [$966$] наблюдения связаны соотношением k=d*sin([$966$])/[$955$]. В Вашем случае максимальный порядок спектра будет при [$966$]=90 [$186$] и составляет kmax=[d/[$955$]]=[7*10-6/(486*10-9)]=14 (квадратные скобки в данном случае указывают на выделение целой части числа).
Спектры порядков k и k+1 не перекрываются, если выполнено условие k([$955$]+[$916$][$955$])<(k+1)([$955$]-[$916$][$955$]), откуда находим [$916$][$955$]<[$955$]/(2k+1). Принимая k+1=kmax=14, получим k=14-1=13, [$916$][$955$]<486/(2*13+1)=18 (нм). Следовательно, искомый интервал составляет [$955$]-[$916$][$955$]<[$955$]<[$955$]+[$916$][$955$], то есть 468 нм<[$955$]<504 нм.
По формуле дифракционной решётки порядок k спектра и угол [$966$] наблюдения связаны соотношением k=d*sin([$966$])/[$955$]. В Вашем случае максимальный порядок спектра будет при [$966$]=90 [$186$] и составляет kmax=[d/[$955$]]=[7*10-6/(486*10-9)]=14 (квадратные скобки в данном случае указывают на выделение целой части числа).
Спектры порядков k и k+1 не перекрываются, если выполнено условие k([$955$]+[$916$][$955$])<(k+1)([$955$]-[$916$][$955$]), откуда находим [$916$][$955$]<[$955$]/(2k+1). Принимая k+1=kmax=14, получим k=14-1=13, [$916$][$955$]<486/(2*13+1)=18 (нм). Следовательно, искомый интервал составляет [$955$]-[$916$][$955$]<[$955$]<[$955$]+[$916$][$955$], то есть 468 нм<[$955$]<504 нм.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
16.04.2019, 15:29
общий
Адресаты:
Незачем тревожить модераторов вопросом, который адресован эксперту, который ответил на Ваш вопрос.
Пишите только в мини-форуме.
Пишите только в мини-форуме.
Об авторе:
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
16.04.2019, 15:40
общий
Адресаты:
ya.anya-semenova почему 3см нигде не применяется ... ???
Мне удалось обойтись без них. Зачем указана ширина решётки, я не знаю.
ya.anya-semenova и от куда взялось 504???
[$955$]+[$916$][$955$]=486+18=504 (нм).
Об авторе:
Facta loquuntur.
Facta loquuntur.
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