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Консультация № 173343
17.10.2009, 09:15
0.00 руб.
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1
Здравствуйте, уважаемые эксперты! Помогите, пожалуйста, решить задачу:
2.30. На дифракционную решетку под углом Θ падает монохроматический свет с длиной волны λ. Найти условие, определяющее направления на главные максимумы, при условии, что d >> mλ (m – порядок спектра).
Должен получиться Ответ: d.cosΘ.(φ - Θ) ≈ mλ.
2.30. На дифракционную решетку под углом Θ падает монохроматический свет с длиной волны λ. Найти условие, определяющее направления на главные максимумы, при условии, что d >> mλ (m – порядок спектра).
Должен получиться Ответ: d.cosΘ.(φ - Θ) ≈ mλ.
Обсуждение
22.10.2009, 00:12
общий
это ответ
Здравствуйте, kot31.
При падении плоской волны на решетку под углом θ полная разность хода для двух соответственных волн равна
∆ = AC – DB = d(sin θ – sin φ),
а условия образования главных максимумов принимают вид
d(sin θ – sin φ) = ±mλ,
или
d ∙ 2 ∙ cos (θ + φ)/2 ∙ sin (θ – φ)/2 = ±mλ. (1)
Если d >> mλ, то θ – φ → 0, и
2 ∙ cos (θ + φ)/2 ∙ sin (θ – φ)/2 ≈ 2 ∙ cos 2θ/2 ∙ (θ – φ)/2 = cos θ ∙ (θ – φ),
а выражение (1) принимает вид
d ∙ cos θ ∙ (θ – φ) ≈ ±mλ.
Полученное выражение совпадает с указанным Вами с точностью до знака.
С уважением.
При падении плоской волны на решетку под углом θ полная разность хода для двух соответственных волн равна
∆ = AC – DB = d(sin θ – sin φ),
а условия образования главных максимумов принимают вид
d(sin θ – sin φ) = ±mλ,
или
d ∙ 2 ∙ cos (θ + φ)/2 ∙ sin (θ – φ)/2 = ±mλ. (1)
Если d >> mλ, то θ – φ → 0, и
2 ∙ cos (θ + φ)/2 ∙ sin (θ – φ)/2 ≈ 2 ∙ cos 2θ/2 ∙ (θ – φ)/2 = cos θ ∙ (θ – φ),
а выражение (1) принимает вид
d ∙ cos θ ∙ (θ – φ) ≈ ±mλ.
Полученное выражение совпадает с указанным Вами с точностью до знака.
С уважением.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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