Course: 14.2 违规 | The Way To Learn

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$A red pencil appears bent in a glass filled with liquid, demonstrating light refraction.$

When a light ray passes at an angle through the boundary between optically different media , the light does not travel in a straight line. The pencil in the glass of liquid shown above is a normal straight pencil. The light that travels from the pencil through the liquid, through the glass, and into the air is bent differently than light from the portion of the pencil that is not in the liquid. Your eye assumes the light from both portions of the pencil moved in a straight line, but the two portions of the pencil do not appear to be lined up. Your eye thinks the pencil is broken.
::当光线从一个角度穿过不同光学介质之间的界线时,光线不会以直线穿行。上面显示的液杯中的铅笔是普通的直铅笔。从铅笔穿透液体、穿过玻璃和进入空气的光线与不在液体中的铅笔部分的光线不同。你的眼睛认为铅笔两部分的光线都是直线移动的,但铅笔的两部分似乎没有排成一行。你的眼睛认为铅笔是折断的。

Refraction of Light
::灯光折射

The of light is different in different media. If the speed of light is slower in a particular medium, that medium is said to be more optically dense . When a wave front enters a new medium at an angle, it will change directions. If the light is entering a more optically dense medium, the light bends toward the normal line. If the light is entering a less optically dense medium, the light will bend away from the normal line. Remember that the normal line is the line perpendicular to the medium interface.
::光在不同的介质中是不同的。如果某一介质的光速较慢, 该介质的光速据说会比较高光密度。当波头在一个角度进入一个新介质时, 它会改变方向。如果光进入一个光密度更高的介质, 光会向正常线弯曲。如果光进入一个光密度较低的介质, 光会从正常线弯曲。记住, 普通线是介质界面的直线。

In the sketch below, light wave fronts are moving upward from the bottom of the page and encounter a boundary into a more optically dense medium. The light waves bend toward the normal line. Because the right end of the wave fronts enter the new medium first, they slow down first. When the right side of the wave front is moving more slowly that the left side, the wave front will change directions.
::在下面的草图中,光波前线正从页面底部向上移动,遇到一个边界,进入一个光密度更高的介质。光波向正常线倾斜。由于波端的右端先进入新介质,它们首先放慢速度。当波端右侧移动较慢,左侧移动较慢时,波面将改变方向。

$Light Refraction At A Boundary Between Two Media With Angles And Normal Line.$

When light is traveling from air into another medium, Snell’s Law states the relationship between the angle of incidence and angle of refraction is
::当光从空气向另一介质移动时,Snell的《法律》规定,发生角度和折射角度之间的关系是:

\begin{aligned} n = \frac{\sin θ_{i}}{\sin θ_{r}} \end{aligned}

::{\fn方正黑体简体\fs18\b1\bord1\shad1\3cH2F2F2F

where $\begin{aligned} θ_{i} \end{aligned}$ is the angle of incidence, $\begin{aligned} θ_{r} \end{aligned}$ is the angle of refraction, and $\begin{aligned} n \end{aligned}$ is the ratio of the two sines and is called the index of refraction . Snell’s Law may be stated that a ray of light bends in such a way that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant.
::当“i”是事件角度时,“r”是事件角度,“r”是折射角度,n是正弦之比,称为折射指数。 Snell的法律可以指出,光线弯曲的方式是,发生角的正弦与折射角之正弦之比是恒定的。

The index of refraction is also related to the relative speeds of light in a vacuum and in the medium.
::折射指数也与真空和介质中光的相对速度有关。

\begin{aligned} n = \frac{speed of light in a vacuum}{speed of light in the medium} \end{aligned}

::n=介质中光光的真空速度中的光速

When a ray of light is traveling from medium into another medium, Snell’s Law can be written as $\begin{aligned} n_{i} \sin θ_{i} = n_{r} \sin θ_{r} \end{aligned}$ .
::当一束光从介质向另一介质移动时, Snell 的法律可以写成 nisini=nrsinr。

Indices of Refraction
Medium	$\begin{aligned} \underline{n} \end{aligned}$
Vacuum	1.00
Air	1.0003
Water	1.36
Ethanol	1.36
Crown Glass	1.52
Quartz	1.54
Flint Glass	1.61
Diamond	2.42

Example 1
::例1

A ray of light traveling through air is incident upon a slab of Flint glass at an angle of $\begin{aligned} {40.0}^{\circ} \end{aligned}$ . What is the angle of refraction?
::空气中一束光线在空气中行走是弗林特玻璃板上发生的事件,角度为40.0。折射的角度是什么?

$\begin{aligned} n = \frac{\sin θ_{i}}{\sin θ_{r}} \end{aligned}$ so $\begin{aligned} \sin θ_{r} = \frac{\sin θ_{i}}{n} = \frac{0.643}{1.61} = 0.399 \end{aligned}$
::{\fn黑体\fs22\bord1\shad0\3aHBE\4aH00\fscx67\fscy66\2cHFFFFFF\3cH808080}那么... {\fn黑体\fs22\bord1\shad0\3aHBE\4aH00\fscx67\fscy66\2cHFFFFFF\3cH808080}那么... {\fn黑体\fs22\bord1\shad0\3aHBE\4aH00\fscx67\fscy66\2cHFFFFFF\3cH808080}... {\fn黑体\fs22\bord1\shad0\3aHBE\4aH00\fscx67\fscy66\2cHFFFFFF\3cH808080}那么...

The angle of refraction $\begin{aligned} = s i n^{- 1} .399 = {23.5}^{\circ} \end{aligned}$
::折射角度=sin-1.399=23.5

Example 2
::例2

What is the speed of light in a diamond?
::钻石的光速是多少?

$\begin{aligned} speed of light in diamond = \frac{speed of light in a vacuum}{n} = \frac{3.00 \times 10^{8} m / s}{2.42} \end{aligned}$
::钻石中的光速=真空中的光速=3.00×108 m/s2.42

$\begin{aligned} speed of light in diamond = 1.24 \times 10^{8} m / s \end{aligned}$
::钻石=1.24×108毫秒/秒

In the Least Time simulation below, you can adjust the sliders so that light travels from air to a denser material like glass or diamond. T hen, drag the incident ray and refracted rays to the correct angles according to Snell’s Law. When you have found the path of least time - a red light ray will shoot out across the both materials! Very exciting!
::在下面最短时间的模拟中,您可以调整滑动器,让光线从空气到玻璃或钻石等更稠密的材料。然后,根据Snell的法律,将事件射线和折射线拖到正确的角度。当你找到最短时间的路径时, 红光线会射向两种材料! 非常令人兴奋!

Effects of Refraction
::违规的影响

Bending the Sun’s Rays
::将太阳的雷光抛在太阳的雷光中

Because air is slightly more optically dense than a vacuum, when sunlight passes from the vacuum of space into our atmosphere, it bends slightly towards the normal. When the sun is below the horizon and thus not visible on a direct line, the light path will bend slightly and thus make the sun visible by refraction. Observers can see the sun before it actually comes up over the horizon, or after it sets.
::由于空气的光密度比真空略高一点,当阳光从空间真空进入大气层时,它会稍微向正常方向弯曲。当太阳在地平线下,因此在直线上看不到太阳时,光线会稍微弯曲,从而通过折射使太阳能看得见。观察家们可以在太阳真正越过地平线之前或者在太阳落成之后看到太阳。

$How Sunlight Refraction Makes The Sun Visible Before And After It Rises.$

Mirages
::幻影

In the Figure , the sun shines on the road, heating the air just above the road. The difference in density between the hot air over the road and the surrounding air causes the hot air to refract light that passes through it. When you look at the road, you see a mirage . What appears to be water on the road is actually light coming from the sky that has been refracted as it passes through the hot air above the road. This phenomenon is common on hot roads and in the desert.
::在图中,阳光照耀着公路,加热公路上方的空气,热空气与周围空气的密度差异导致热空气粉碎穿过公路的光线。你看路时,看到海市图。看路时看似是海景。看路面的水实际上是从天上发出的光,在路面上方的热空气中经过时,天上又重新变红了。这种现象在热路和沙漠中司空见惯。

$A road with a mirage effect, appearing to reflect water due to light refraction.$

Summary
::摘要

The speed of light is different in different media.
::光的速度在不同的介质中是不同的。

When a wave front enters a new medium at an angle, it will change directions. If the light is entering a more optically dense medium, the light bends toward the normal line. If the light is entering a less optically dense medium, the light will bend away from the normal line.
::当波头以一个角度进入一个新介质时,它会改变方向。如果光线进入一个光密度更高的介质,光线会向正常线弯曲。如果光线进入一个光密度较低的介质,光会从正常线弯曲。

When light is traveling from air into another medium, Snell’s Law states that $\begin{aligned} n = \frac{\sin θ_{i}}{\sin θ_{r}} \end{aligned}$ .
::当光从空气向另一介质飘移时,

The index of refraction is also related to the relative speeds of light in a vacuum and in the medium. $\begin{aligned} n = \frac{speed of light in a vacuum}{speed of light in the medium} \end{aligned}$
::折射指数也与真空和介质中的光的相对速度有关。 n=介质中光的真空速度中的光速。

When a ray of light is traveling from one medium into another medium, Snell’s Law can be written as $\begin{aligned} n_{i} \sin θ_{i} = n_{r} \sin θ_{r} \end{aligned}$ .
::当一束光从一个介质传到另一个介质时, Snell 的法律可以写成 nisini=nrsinr。

Review
::回顾

Light moving through air is incident on a piece of crown glass at an angle of $\begin{aligned} 45^{\circ} \end{aligned}$ . What is the angle of refraction?
::光在空气中移动是在45°Q角的一小块皇冠玻璃上发生的折射角度是什么?

A ray of light passes from air into water at an incident angle of $\begin{aligned} 60^{\circ} \end{aligned}$ . Find the angle of refraction.
::从空气到水的一线光线以60°Z的事故角度向水中射入60°C 寻找折射角度

Light passes from water into a block of transparent plastic. The angle of incidence from the water is $\begin{aligned} 31^{\circ} \end{aligned}$ and the angle of refraction in the block is $\begin{aligned} 27^{\circ} \end{aligned}$ . What is the index of refraction for the plastic?
::光从水中传入一个透明塑料块。水的发生角为31°C,而块的折射角为27°C。塑料的折射指数是多少?

The index of refraction of water is 1.36. What is the speed of light in water?
::水的折射指数是1.36 水的光速是多少?

If the speed of light in a piece of plastic is $\begin{aligned} 2.00 \times 10^{8} m / s \end{aligned}$ , what is the index of refraction for the plastic?
::如果一块塑料中的光速为2.00×108 m/s,那么塑料的折射指数是什么?

Section outline

General

折中

Refraction of Light ::灯光折射

Example 1 ::例1

Example 2 ::例2

Effects of Refraction ::违规的影响

Bending the Sun’s Rays ::将太阳的雷光抛在太阳的雷光中

Mirages ::幻影

Summary ::摘要

Review ::回顾