Name: 物理 52 屈折とスネルの法則（11の1） スネルの法則入門 (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.

ELEKTRON-Lineへようこそ。ここでは、屈折と呼ばれる光学のもう一つの性質についてお話しします。

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.

屈折が意味するのは、光線がある媒質から別の媒質、たとえば空気からガラスへと移動するとき、その境界を越えると何かが起こるということだ。

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.

なぜ何かが起こるかというと、ガラスには、それを通過する光の速度に影響を与える性質があるからだ。

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?

では、光が空気中を飛んでいるときの光速がcに等しいとすると、光がガラスの中を横切ったときの光速はどうなるのだろうか？

Well that depends on something called the index of refraction.

それは屈折率と呼ばれるものによるね。

だから、それを書き留めておこう。

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

そして、それが何であるかを示すために、nという文字を使う。

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

そこで、屈折率を示すために小さなnという文字を使う。

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.

光線がある媒質から別の媒質へ、つまり媒質1から媒質2へ進むとき、最初の媒質、つまり空気の屈折率をn1、ガラスの屈折率をn2と呼ぶことにします。

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.

さて、空気の屈折率はたまたま1であり、他の物質では1以上になる傾向があるため、ガラスの屈折率は通常1.5か1.6となる。

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

では、この2つの媒質を通る光の旅に関しては、どういうことになるのだろうか？

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.

空気中を伝わる光の速度がcだとすると、ガラスの中を伝わる光の速度はcを屈折率で割ったものになる。

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.

つまりこの場合、cは10の3乗で秒速8メートルとなり、それを1.6で割ると新しい光の速度が得られる。

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.

電卓を持ってこなかったことを思い出したので、すぐに電卓を取ってきます。

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.

さて、電卓を手に入れたので、光がガラスを通過する速度を調べてみよう。ガラスの屈折率は1.6なので、3を1.6で割ると1.875となる。

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?

ここで、光線がある媒質から別の媒質へ進むとどうなるかというと、ここでは空気と水、つまり2つの異なる媒質があり、空気と水の屈折率は1、水と2の屈折率は1に等しい。33 さて、光は表面に対して垂直または法線の境界をまっすぐ進むのではなく、法線に対して角度をつけて進むことに注意してください、屈折率が小さい方から大きい方へと進む光の場合、屈折はいわゆる法線方向へと進むので、法線と光線の間の角度は小さくなり、光は次のようになります。

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?

簡単な例を挙げてみよう......例えば、シータ1が30度に等しいとすると、シータ2はどうなると思う？

 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

スネルの法則によれば、θ1の正弦のn1倍はθ2の正弦のn2倍に等しく、我々が求めようとしているのはθ2の正弦を求めることである。そして最後に、θサブ2を求めるためにアークサインを取る。つまり、θサブ2はこの全体の逆数、またはアークサインに等しい、n1は1、n2は1です。33この場合、空気から水中へ入るので、シータサブ2はn1のアークサインに等しいと言える。33と30度の正弦を掛け合わせたものである。1度となり、これが屈折角と呼ばれるものです。では、法線と光線の間の角度が90度、つまり0度のとき、光は屈折す

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物理 52 屈折とスネルの法則（11の1）スネルの法則入門 (Physics 52 Refraction and Snell's Law (1 of 11) Introduction to Snell's Law)

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物理 52 屈折とスネルの法則（11の1） スネルの法則入門 (Physics 52 Refraction and Snell's Law (1 of 11) Introduction to Snell's Law)

significant

matter

straight

concept

物理 52 屈折とスネルの法則（11の1）スネルの法則入門 (Physics 52 Refraction and Snell's Law (1 of 11) Introduction to Snell's Law)