Name: 物理 52 折射與斯涅耳定律（共 11 頁，第 1 頁） 斯涅耳定律簡介 (Physics 52 Refraction and Snell's Law (1 of 11) Introduction to Snell's Law)
Uploaded: 2024-10-02T09:19:02.000Z
Duration: 6 min 19 s

Welcome to ELEKTRON-Line and here we're going to talk about another property in optics called refraction.

歡迎來到 ELEKTRON-Line，在這裡我們將討論光學中的另一個特性--折射。

And what refraction means is that when a ray of light moves from one medium to another medium for example from air to glass something happens once it crosses that boundary.

折射的意思是，當光線從一種介質移動到另一種介質時，例如從空氣移動到玻璃，一旦光線越過邊界，就會發生一些事情。

The reason why something happens is that there's some property about glass that does something to the speed of light as it travels through it.

之所以會出現這種情況，是因為玻璃的某種特性會影響光速。

So if we know that the speed of light right here is equal to c when light is traveling in the air, what is the speed of light equal to once it traverses into glass?

那麼，如果我們知道光在空氣中傳播時，這裡的光速等於 c，那麼一旦光穿越玻璃，光速又等於多少呢？

Well that depends on something called the index of refraction.

And to indicate what that is we use the letter n.

So we use the letter small n to indicate the index of refraction.

是以，我們用字母小 n 來表示折射率。

Note when the ray travels from one medium to another as going from medium 1 to medium 2, I'll call this n1, the index of refraction of the first medium, meaning air, and n2 is going to be the index of refraction of glass.

請注意，當光線從一種介質傳播到另一種介質時，就像從介質 1 傳播到介質 2 一樣，我將其稱為 n1，即第一種介質（即空氣）的折射率，而 n2 將是玻璃的折射率。

Now for air the index of refraction happens to be 1 and for any other substance it tends to be more than 1 so for glass it's typically maybe like a 1.5 or 1.6 so let's call it 1.6.

現在，空氣的折射率恰好是 1，而其他物質的折射率往往大於 1，所以玻璃的折射率通常是 1.5 或 1.6，我們稱之為 1.6。

Okay, then what does that mean as far as the travel of light through these two mediums?

好吧，那麼光在這兩種介質中的傳播意味著什麼呢？

Well if the velocity of light is c when it travels through air then for the velocity once it travels in the glass is equal to c divided by the index of refraction.

如果光在空氣中傳播時的速度是 c，那麼光在玻璃中傳播時的速度就等於 c 除以折射率。

So in this case we know that c is 3 times 10 to the 8 meters per second and then we divide that by 1.6 and that will give us then the new velocity of light.

是以，在這種情況下，我們知道 c 是 10 的 3 倍，即每秒 8 米，然後除以 1.6，就得出了新的光速。

And I just remembered I did not bring my calculator so let me go get my calculator real quick and I'll be right back.

我剛想起來我沒帶計算器，所以讓我趕緊去拿計算器，馬上就回來。

Now that I have my calculator let's find out how fast light travels through glass, well for glass that has an index of refraction of 1.6 so we take 3 divided by 1.6 and we get 1.875 so this is equal to and let me go like this equal to 1.875 times 10 to the 8 meters per second so it's a significant slowdown still fast but you can see that light does travel at a different speed and there's a medium other than air or just free space.

現在我有了計算器，讓我們來看看光在玻璃中的傳播速度，玻璃的折射率為 1.6，所以我們用 3 除以 1.6，得到 1.875，這就等於 1.875 乘以 10 等於每秒 8 米，所以速度明顯減慢，但仍然很快，但你可以看到光的傳播速度確實不同，而且除了空氣或自由空間之外，還有其他介質。

So what happens now when a ray of light travels from one medium to another and here we have air and water, doesn't matter just two different mediums and the index of refraction for air and 1 equals 1 for water and 2 equals 1.33 Now notice that the light does not travel straight across the boundary at a line that's perpendicular or normal to the surface, it travels at an angle relative to the normal and when it crosses a boundary like that something else happens to the light besides it slowing down, it also changes direction, it bends or it refracts as we call it and in the case of light that travels from an index of refraction which is smaller to an index of refraction which is larger the bending will be what we call towards the normal so the angle between the normal and the ray will become smaller and so the light will do something like this and this will now be theta sub 2 notice that theta sub 2 is indeed smaller than theta sub 1 Well how do we actually find out what those angles are?

那麼，當光線從一種介質傳播到另一種介質時，會發生什麼呢？這裡有空氣和水，無所謂，只是兩種不同的介質，空氣的折射率 1 等於 1，水的折射率 2 等於 1。33 現在請注意，光線並不是直線穿過與表面垂直或法線的邊界，它是以相對於法線的角度穿過邊界的、當光線從折射率較小的地方傳播到折射率較大的地方時，會發生我們所說的向法線彎曲，是以法線和光線之間的夾角會變小，所以光線會發生類似這樣的變化，這就是θ sub 2，注意θ sub 2確實比θ sub 1小。

Let's do a quick example let's say for example that theta 1 is equal to 30 degrees then what do you think theta 2 will be equal to?

舉個簡單的例子，比如說θ 1 等於 30 度，那麼你認為θ 2 會等於多少度？

 Well it turns out that Snell's law enables us to do that and Snell's law says that n1 times the sine of theta 1 equals n2 times the sine of theta sub 2 and again what we're trying to find is we're trying to find the angle sine of theta sub 2 which means we have to algebraically solve for that angle so we're first going to flip the equation around so we can say that n2 times the sine of theta 2 equals n1 times the sine of theta sub 1 then the next step is we're going to divide both sides by n sub 2 so we have the sine of theta sub 2 is equal to n1 over n2 times the sine of theta sub 1 and finally to find theta sub 2 we take the arc sine so theta sub 2 equals the inverse or arc sine of this whole thing right here which is n1 over n2 times the sine of theta sub 1 now plug in the values that we have so we know that theta sub 1 is 30, n1 is 1 and n2 is 1.33 in this particular case because it's from air into water we can say that theta sub 2 is equal to the arc sine of n1 which is 1, n2 which is 1.33 and times the sine of 30 degrees okay let's find out what that's equal to so you take the sine of 30 that should be 0.5 divide that by 1.33 and then take the arc sine of that and we get 22.1 degrees so theta sub 2 is equal to 22.1 degrees and that's what we call the angle of refraction let's write that down so that's called the angle of refraction okay so notice that when the angle is 90 degrees or I should say 0 degrees between the normal and the ray there's no bending of light the light goes straight through the only thing that happens is that it slows down relative to the index of refraction in this case let me just put down v sub 2 and that's the velocity in the second region is dependent upon the index of refraction in the second region but if the ray comes in at an angle then not only does it slow down once it crosses the boundary it also changes direction it has a new direction the direction is different from the angle of incidence and using Snell's law is how we find what that angle is alright so there's a nice little introduction to the concept of refraction

斯涅爾定律告訴我們，n1 乘以θ 1 的正弦等於 n2 乘以θ 2 的正弦，而我們要找的是θ 2 的角度正弦，這意味著我們必須用代數方法求解這個角度。下一步，我們要把兩邊都除以 n 次 2，這樣，θ 次 2 的正弦等於 n1 乘以 n2 再乘以θ 次 1 的正弦，最後，為了求出θ 次 2，我們取弧正弦，所以θ 次 2 等於這個整體的逆正弦或弧正弦，也就是 n1 乘以 n2 再乘以θ 次 1 的正弦、n1 是 1，n2 是 1。33 在這種特殊情況下，因為是從空氣進入水中，我們可以說，θ 子 2 等於 n1

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物理 52 折射與斯涅耳定律（共 11 頁，第 1 頁）斯涅耳定律簡介 (Physics 52 Refraction and Snell's Law (1 of 11) Introduction to Snell's Law)

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物理 52 折射與斯涅耳定律（共 11 頁，第 1 頁） 斯涅耳定律簡介 (Physics 52 Refraction and Snell's Law (1 of 11) Introduction to Snell's Law)

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物理 52 折射與斯涅耳定律（共 11 頁，第 1 頁）斯涅耳定律簡介 (Physics 52 Refraction and Snell's Law (1 of 11) Introduction to Snell's Law)