3-2__全反射和棱镜
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§3-2 全反射和棱镜 一、全反射 现象:当光从光密媒质入射到光疏媒质时,存在 一个特殊的角度ic,如果入射角≥ ic , 则光全部被 反射。 回顾光线传播三定律: 如何确定ic呢? 1、光在均匀媒质中沿直线传播 2、反射定律、折射定律 √ 3、光的独立传播原理和光路可逆原理
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i1增大 折射定律:
n1 sin i1 = n 2 sin i 2
1 2
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当n1>n2时, i1
i2也 增大
光由光密->光疏媒质时,存在全反射临界角: 令:i2=90°,得: i c = sin −1 ?
n2 n1
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全反射的应用很广泛:
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⑴ 全反射棱镜——横截面是等腰直角三角形的棱镜
光从直角面垂直到达 斜面时的入射角为45°, 大于ic,光线无损失地 偏转90° 。
光从斜面垂直入射,可以 使光线无损失的逆转180° 已知玻璃的折射率约为1.5,计算可得由玻璃到 空气的全反射临界角是 arcsin(1/1.5)=42° .
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如果入射光从一物发 出,经两次全反射后成倒 立的像,常用于潜望镜和 望远镜。
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⑵光学纤维。
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光学纤维的优点: ①可以弯曲,芯线直径很小,弯曲时仍可以全反射。 ②信息量大,一根光纤理论上可通电话100亿路(1010)
直径为几微米~几十微米的芯线,外包透明介质。 n0 n2 n1 cladding core n1>n2>n0 光从端面入射时,入射角如果大于全反射临界角, 光线在芯线和包层的界面上发生全反射,光可以从一 端无能量损失地传到另一端。 (子午面上的光线)
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③石英制成,原料丰富。 光纤的用途: 传送光、图象 ——内窥镜 传送光学信息 ——光纤通信
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Swimming pool experience:
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The next time you go swimming, do the following experiment (safely!): From underwater, look at people or trees outside the water. You will see that you can see them when you view with your eyes at small angles relative to the normal to the water surface. But as you look at larger angles, you find that the water surface suddenly appears weird, somewhat like liquid mercury. This occurs because the water surface reflects like a mirror so that you are not able to observe anything outside the pool. This is a consequence of total internal reflection. (If you will not be swimming for a while, you can also check this by looking at the water-air surface of a fish tank from below.)
Medical diagnoses: A standard method of medical imaging utilizes ultrasonic sound echocardiography,ultrasonic sound waves produce images of inner body organs (along with many other applications). A wave of ultrasonic sound sent into the body is refracted and reflected as it passes through parts of the body of different density. The wave reflected from a specific organ is observed by a detector and produces an image. The manner in which the ultrasonic sound waves get reflected and refracted is similar to the case for light that we have considered.
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An important difference between light and sound waves is that soundwaves propagate faster in water than in air. (With light, it is the other way around!) This means that, for sound, water has a lower index of refraction than air! Therefore, total internal reflection occurs going from air to water. To enable the sound waves to get into the body requires having no air between the source and the body, usually accomplished by putting a layer of gel between the sound head and the body. This also means you cannot send ultrasonic sound trough air-filled organs (like the lungs).
二、等腰三棱镜的最小偏向角 等腰三棱镜的横截面为等腰三角形
等腰三棱镜的第一个作用是使光线偏折。
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1、偏向角 (空气中的棱镜) 光线在横截面内,从一个侧面入射,经两次折射 从另一个侧面出射。 偏向角的定义:由入射 光线方向转向出射光线方 A 向的角度,用θ表示。 由几何关系可得:
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θ = i1 + i1 '− A
已知i1时,i1'可按下面 步骤求出:
A
θ i1 i2 i2'
(1)
( 2)
θ i1' i1 i2 i2'
sin i1 = n sin i 2
i2'= A − i2 sin i 1 ' = n sin i 2 '
i1'
θ = ( i 1 − i 2 ) + (i 1 '− i 2 ' )
( 3)
∵i2 + i2'= A ∴ θ = i 1 + i 1 '− A
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所以,偏向角的大小由入射角 i1 决定: θ = θ(i1)
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2、最小偏向角
θ = i1 + i1 '(1A −)
sin i1 = n sin i 2
三、棱镜的色散
sin(
理论和实验都表明偏向角有一个最小值 由极值条件
di ' dθ = 0 => 1 + 1 = 0 di 1 di 1
θ0 + A A ) = n sin( ) 2 2
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棱镜的第二个作用是使入射白光的各色光散开, 沿不同方向出射,这种性质称为棱镜的色散。(详见
6.4节)
进一步可解出: i1=i1'
此时也有: i 2 = i 2 ' = A 2
入射光线和出射光线对称。
棱镜产生色散的原因是介质的折射率与波长有关: 棱镜产生色散的原因? n=n(λ) 例如,玻璃在可见光波段的折射率随波长的增加而 减小。 (p.396,p.399 色散曲线)
dn dλ
θ +A A ) = n sin( ) ∴最小偏向角θ0满足: sin( 0 2 2
称为介质的色散
实验中可以用测得的θ0,求出n或A。 演示实验: 最小偏向角
水中的棱 镜如何?
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利用介质的色散性质,可以制作棱镜分光仪器, 如:光谱仪,分光计等。
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1、棱镜分光系统的构造和原理
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2、棱镜的角色散
设最小偏向角为θ0(λ),角色散的定义为:
Dθ = dθ 0 ( λ ) dθ 0 ( λ ) dn = ⋅ dλ dn dλ
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L2 L1
f
观察屏
θ +A A ) = n sin( ) ∵ sin( 0 2 2
?
∴n =
sin(
待测光源发出的光经透镜 L1 后出射平行光, 平行光经棱镜两次折射后,出射的各色光仍是平行光, 但偏向角不同,各色光分别交于观察面上的不同点。 如果待测光源为缝光源(垂直纸面),则在观察面上每 种颜色的光将会聚成一条线(谱线)。 next
A θ0 + A 1 1 − n 2 sin 2 ( ) dn 2 cos( 2 ) 2 ∴ = = A A dθ 0 sin( ) 2 sin( ) 2 2 A 2 sin( ) dn 2 ⋅ ∴ Dθ = dλ 2 2 A 1 − n sin ( ) 2
θ0 + A ) 2 A sin( ) 2
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作业: p. 222 4, 5
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