Inside one raindrop一顆雨滴裡面
Follow one ray as it enters near the edge of the drop and comes back out at about 42 degrees.
跟著一道從水滴邊緣附近射進去的光，看它在約 42 度的方向回頭射出。
How Things Work · Unit 3 · Lesson 10 · 萬物原理 單元三 第十課
How Does a Rainbow Form?彩虹是怎麼形成的？
A rainbow is sunlight bent and bounced inside millions of raindrops. Follow one ray through a 3D raindrop, then stand with the Sun behind you and watch falling rain light up in a 42-degree circle.
彩虹是陽光在幾百萬顆雨滴裡轉彎、反射出來的光。在 3D 雨滴裡跟著一道光走，再背對太陽站好，看落下的雨在 42 度的圓上亮起來。
Big idea · 一句話看懂
Sunlight bends as it enters a raindrop, reflects off the back, and bends again as it leaves, and water bends each color a slightly different amount. So the colors come back out at slightly different angles, all close to 42 degrees from the point straight opposite the Sun. That is why a rainbow is part of a circle and is always on the side of the sky away from the Sun.
陽光射進雨滴時轉彎，在水滴背面反射，出來時再轉彎；水讓每種顏色轉彎的程度差一點點。所以各色從稍微不同的角度回頭射出，全都在「太陽正對面那一點」外圍約 42 度的地方。這就是為什麼彩虹是圓的一部分，而且永遠在背對太陽的那一邊。
3D Model · 3D 模型
Light Inside a Raindrop 雨滴裡的光
Drag to turn the model, and scroll or pinch to zoom. In “You and the rain,” the Sun is behind you: slide the Sun higher or lower and watch which falling drops flash with color. In “One raindrop,” slide where the light enters the drop and read the angle it comes back at, or turn on many rays to see the light crowd near 42 degrees.
拖曳可以旋轉模型，滾輪或雙指可以縮放。在「你和雨」裡，太陽在你背後：把太陽拉高或拉低，看哪些落下的雨滴閃出顏色。在「一顆雨滴」裡，移動光射入的位置，讀光回頭的角度；或打開「很多道光」，看光怎麼擠在 42 度附近。
Raindrops drawn much bigger than real; the angles are calculated · 雨滴畫得比真的大很多；角度是算出來的
Drag to turn · 拖曳旋轉 Scroll or pinch to zoom · 滾輪／雙指縮放
This 3D model needs WebGL, which this browser does not support. The reading and the cards below still explain everything.
這個瀏覽器不支援 WebGL，無法顯示 3D 模型；下方的課文與卡片一樣能看懂。
- Colors: each color leaves the drops at a slightly different angle, red at about 42 degrees and violet at about 41
顏色：各色從雨滴出來的角度稍有不同，紅約 42 度、紫約 41 度 - Yellow lines: sunlight coming from behind you
黃線：從你背後照來的陽光 - Dashed white lines: the 42-degree cone from your eye to the rainbow
白色虛線：從你的眼睛到彩虹、張開 42 度的圓錐 - Yellow dot: the point straight opposite the Sun, the center of the rainbow circle
黃點：太陽的正對面，也就是彩虹那個圓的圓心
A diagram: the raindrop is enlarged and drawn as a flat slice, and the rain falls about 20 meters in front of you. The angles are calculated with the law of refraction from how much water bends each color (red bends the least, violet the most). Real rainbows also depend on the size of the drops and on how bright the sunlight is.
這是示意圖：雨滴放大並畫成一個平面切面，雨落在你前方約 20 公尺。角度是用折射定律、依照水讓各色光轉彎的程度算出來的（紅光轉得最少、紫光最多）。真正的彩虹還跟雨滴大小、陽光強弱有關。
Model drawn by My Culture Connect as a teaching diagram. Rainbow angles and history from Wikipedia, “Rainbow”, including its values for how much water bends red and violet light. · 模型由人師教育協會自繪示意；彩虹的角度與歷史依維基百科「Rainbow」條目，水對紅光與紫光的折射率也取自該條目。
Reading · 英文閱讀
10
Unit 10: How Does a Rainbow Form?
A summer afternoon shower ends, the Sun comes out, and suddenly a rainbow arches across the sky. Look closely and you will notice something every time: the Sun is behind you, and the rainbow is in front of you. Try to walk to the end of a rainbow, and it moves away as you move. A rainbow is not an object sitting in one place. So what is it?
夏天午後一場陣雨剛停，太陽露臉，天空突然掛起一道彩虹。仔細看，你每次都會發現同一件事：太陽在你背後，彩虹在你前面。想走到彩虹的盡頭，你一走它就跟著退。彩虹不是待在某個地方的東西，那它到底是什麼？
People have wondered about rainbows for a very long time. More than 900 years ago in Song dynasty China, the scholar Shen Kuo wrote that rainbows form when sunlight meets raindrops in the air. Around 1300, Kamal al-Din al-Farisi in Persia explained that light bends twice and reflects inside each drop, and he tested the idea with a glass sphere filled with water. In 1637, the French thinker René Descartes measured the angles with a large water-filled glass sphere of his own.
人們對彩虹好奇了很久很久。九百多年前，中國宋朝的沈括就寫道：彩虹是陽光碰到空氣中的雨滴形成的。大約 1300 年，波斯的法里西解釋光在每顆雨滴裡轉彎兩次、反射一次，還用一個裝滿水的玻璃球做實驗。1637 年，法國的笛卡兒也用一個裝水的大玻璃球，量出了光出來的角度。
Here is what happens inside one raindrop. Sunlight enters the drop and bends, which is called refraction. It crosses the drop, reflects off the back, and bends again as it leaves, heading back toward the side the Sun is on. Light that enters at different places comes back at different angles, but a lot of it piles up close to 42 degrees, so the light is brightest there. This angle does not depend on the size of the drop.
一顆雨滴裡發生的事是這樣的：陽光射進雨滴時轉彎，這叫做「折射」；穿過水滴、在背面反射，出來時再轉彎一次，往太陽那一側射回去。從不同位置射進來的光，回頭的角度不一樣，但有很多都擠在 42 度附近，所以那裡最亮。這個角度跟雨滴大小無關。
Water bends each color by a slightly different amount. Red light bends the least and comes back at about 42 degrees, while violet bends the most and comes back at about 41 degrees. When you look at the sky, the drops that send red light into your eyes form an outer ring, and the drops that send violet form a ring just inside it. That is why red is on the outside of a rainbow and violet is on the inside.
水讓每種顏色轉彎的程度差一點點：紅光轉得最少，回頭約 42 度；紫光轉得最多，回頭約 41 度。你看天空時，把紅光送進你眼睛的雨滴排成外圈，把紫光送進來的雨滴排成緊貼在內側的一圈。所以彩虹外側是紅色、內側是紫色。
All the drops that send color to your eyes lie on a circle around the point straight opposite the Sun, where the shadow of your head points. That is why a rainbow is part of a circle and is always opposite the Sun. When the Sun is higher than about 42 degrees, the whole circle is below the horizon, so rainbows are usually seen in the morning or late afternoon. From an airplane, you can sometimes see the whole circle.
所有能把顏色送進你眼睛的雨滴，都排在一個圓上，圓心就是太陽的正對面，也就是你頭的影子所指的地方。所以彩虹是圓的一部分，而且永遠在太陽的對面。太陽高過約 42 度時，整個圓都沉到地平線以下，所以彩虹通常出現在早上或傍晚。從飛機上，有時能看到整個圓。
Sometimes a second, fainter rainbow appears outside the first, at about 50 to 52 degrees. Its light reflects twice inside each drop, so its colors are in the opposite order, with red on the inside. The darker sky between the two bows is called Alexander's band, after the Greek thinker Alexander of Aphrodisias, who described it about 1,800 years ago. And because each person's eyes catch light from a different set of drops, no two people ever see exactly the same rainbow.
有時候，第一道彩虹外面還會出現一道比較淡的第二道彩虹，大約在 50 到 52 度。它的光在每顆雨滴裡反射兩次，所以顏色順序相反，紅色在內側。兩道彩虹之間比較暗的天空叫做「亞歷山大暗帶」，名字來自大約 1,800 年前描述它的希臘學者亞歷山大。還有，每個人的眼睛接收的是不同一批雨滴的光，所以沒有兩個人看到的彩虹完全一樣。
Read aloud · 課文朗讀
Questions · 閱讀理解
What three things happen to sunlight inside a raindrop to make a rainbow?
It bends as it enters the drop, reflects off the back of the drop, and bends again as it leaves.
Why is red on the outside of a rainbow and violet on the inside?
Red light comes back at a larger angle, about 42 degrees, than violet light, about 41 degrees, so the drops that send red to your eyes form the outer ring.
Why do you rarely see a rainbow at midday?
At midday the Sun is often higher than about 42 degrees, so the whole rainbow circle is below the horizon.
Words & Phrases · 生字及片語
raindrop(n.)雨滴A raindrop slid down the window.一顆雨滴沿著窗戶滑下來。bend(v.)彎曲；轉彎A straw looks bent in a glass of water.吸管放在一杯水裡，看起來像是彎的。reflect(v.)反射The mirror reflects the light from the window.鏡子反射窗外的光。angle(n.)角度The ramp rises at a gentle angle.這條斜坡以平緩的角度往上。circle(n.)圓；圓圈We sat in a circle on the floor.我們在地上圍成一個圓圈坐著。arch(v.)成拱形；橫跨A bridge arches over the river.一座橋拱形地橫跨河面。opposite(adj.)對面的；相反的The library is on the opposite side of the street.圖書館在街道的對面。faint(adj.)淡的；微弱的We could see a faint light far away.我們看得到遠處一道微弱的光。
Quick Check · 小測驗
1. Where is the Sun when you see a rainbow?
2. What happens to sunlight inside a raindrop?
3. Which color is on the outside of a regular rainbow?
4. About how big is the angle of a rainbow from the point opposite the Sun?
5. What is special about a second rainbow?
Try It in the Model · 在模型裡試試
Four ways to look 四種看法
Turn on “Second rainbow” in the model to see the fainter bow at about 51 degrees, with its colors reversed.
在模型裡打開「第二道彩虹」，看約 51 度、顏色相反、比較淡的那一道。
Many rays at once一次很多道光
Rays enter all over the drop, but many of them leave close to 42 degrees. That bright crowd is the rainbow.
光從水滴各處射進去，但很多都在 42 度附近出來。擠在一起的亮光，就是彩虹。
Sun behind you背對太陽
Only the falling drops on a 42-degree circle flash color, red outside and violet inside.
只有落在 42 度那一圈上的雨滴會閃出顏色，紅在外、紫在內。
Midday Sun中午的太陽
The Sun is too high, so the whole rainbow is below the horizon and the rain stays plain.
太陽太高，整道彩虹沉到地平線下，雨就只是普通的雨。
Rainbows by the Numbers · 彩虹的數字
Angles that make a rainbow 形成彩虹的角度
Every rainbow follows the same few angles, no matter how big the raindrops are.
不管雨滴多大，每一道彩虹都遵守同樣幾個角度。
42°red, outside · 紅色，在外側
Red light comes back about 42 degrees from the point opposite the Sun.紅光從太陽正對面那一點往外約 42 度。
41°violet, inside · 紫色，在內側
Violet bends more, so it comes back at a slightly smaller angle.紫光轉彎轉得多，回頭的角度小一點。
51°second rainbow · 第二道彩虹
Light that reflects twice makes a fainter bow at about 50 to 52 degrees, colors reversed.反射兩次的光，在約 50 到 52 度形成較淡、顏色相反的彩虹。
1.33how much water bends light · 水的折射率
From about 1.330 for red to 1.343 for violet: that small difference spreads out the colors.紅光約 1.330、紫光約 1.343：差這麼一點點，就把顏色分開了。
1637Descartes's glass sphere · 笛卡兒的玻璃球
Descartes measured the angles with a large glass sphere filled with water.笛卡兒用一個裝水的大玻璃球量出了角度。
Myth vs. Fact · 常見迷思
Four things people get wrong 四個常見的誤會
✗ Myth · 迷思You can walk to the end of a rainbow.可以走到彩虹的盡頭。
✓ Fact · 事實A rainbow is light coming at a certain angle from many raindrops. When you move, a different set of drops makes your rainbow, so it moves with you.彩虹是從很多雨滴、以特定角度射來的光。你一移動，換成另一批雨滴替你做彩虹，所以它會跟著你走。
✗ Myth · 迷思A rainbow is shaped like an arch.彩虹本來就是拱橋的形狀。
✓ Fact · 事實A rainbow is really a circle. The ground usually hides the lower part, but from an airplane you can sometimes see the whole ring.彩虹其實是一個圓，只是地面通常擋住了下半部；從飛機上，有時能看到一整圈。
✗ Myth · 迷思Two friends standing side by side see the same rainbow.並肩站的兩個朋友看到的是同一道彩虹。
✓ Fact · 事實Each person's eyes catch light from a different set of raindrops, so no two people see exactly the same rainbow.每個人的眼睛接收的是不同一批雨滴的光，所以沒有兩個人看到的彩虹完全一樣。
✗ Myth · 迷思Bigger raindrops make a bigger rainbow.雨滴越大，彩虹越大。
✓ Fact · 事實The 42-degree angle depends on how much water bends light, not on the size of the drops.42 度這個角度取決於水讓光轉彎的程度，跟雨滴大小無關。
Remember It · 記憶口訣
Rainbows in a sentence 一句話記住彩虹
Sun behind, rainbow ahead太陽在背後，彩虹在前面
Turn your back to the Sun to look for a rainbow.
想找彩虹，就背對太陽。
Bend, bounce, bend轉彎、反射、再轉彎
That is the path of sunlight inside a raindrop.
這就是陽光在雨滴裡走的路。
Forty-two四十二度
The rainbow is a circle 42 degrees around the point opposite the Sun.
彩虹是繞著太陽正對面、半徑 42 度的圓。
Red rides on top紅色在最外圈
In the main rainbow, red is on the outside; in the second one, it is on the inside.
主虹紅色在外側；第二道彩虹紅色在內側。
Safety First · 安全提醒
Before you try anything 動手之前先讀
- Never look straight at the Sun while you look for a rainbow. Keep your back to it.找彩虹時絕不直視太陽，要背對著它。
- When you make a rainbow with a garden hose, stand with your back to the Sun, and never spray people, pets, or anything electrical.用水管噴霧做彩虹時，背對太陽站，絕不朝人、寵物或任何電器噴。
- Wet ground is slippery. Wear shoes and walk, don't run.地面濕了會滑，要穿鞋、用走的，不要跑。
- If you hear thunder, go indoors right away. Look for rainbows only after the storm has passed.聽到打雷就馬上進到室內，等暴風雨過了再找彩虹。
- Glass can break. Ask an adult to help with the glass of water in the activity.玻璃會破，活動裡的水杯請大人幫忙拿。
Classroom Activity 1 · 課堂活動一
Make Your Own Rainbow 自己做一道彩虹
You need · 準備材料
- A garden hose with a spray nozzle, or a spray bottle一條有噴頭的水管，或一個噴霧瓶
- A sunny morning or late afternoon一個晴朗的早上或傍晚
Steps · 步驟
- Stand with your back to the Sun, so your shadow points in front of you.背對太陽站好，讓你的影子落在前方。
- Spray a fine mist in front of you, above the shadow of your head.在前方、你頭的影子上方噴出細細的水霧。
- Look for the rainbow. Is red on the outside? Point to the center of its circle: it should be the shadow of your head.找找彩虹：紅色在外側嗎？指出這個圓的圓心，應該就是你頭的影子。
- Try it at noon. Can you still see a rainbow on the ground in front of you? Why or why not?中午再試一次：還看得到嗎？為什麼？
A spray bottle works on a balcony too. Keep the mist away from phones and power outlets.
在陽台用噴霧瓶也可以，水霧要遠離手機和插座。
Classroom Activity 2 · 課堂活動二
A Rainbow from a Glass of Water 一杯水做出的彩虹
You need · 準備材料
- A clear glass of water (an adult holds it)一杯透明的水（由大人拿）
- A sheet of white paper一張白紙
- A sunny windowsill or a bright flashlight有陽光的窗台，或一支亮的手電筒
Steps · 步驟
- Set the glass at the edge of a sunny windowsill, with the paper on the floor below.把水杯放在有陽光的窗台邊，下方地上鋪白紙。
- Move the paper until a small band of colors appears on it.移動白紙，直到上面出現一小條彩色光帶。
- Which color is bent the most? Which is bent the least? Compare with the model.哪個顏色轉彎最多？哪個最少？和模型比一比。
- Talk about it: how is the glass of water like a raindrop, and how is it different?討論：這杯水哪裡像一顆雨滴？哪裡不一樣？
The colors appear faintly; a darker room and stronger sunlight help.
顏色會很淡，房間暗一點、陽光強一點比較容易看到。
Sources · 資料出處
Facts and numbers on this page were checked against these sources (October 2026). · 本頁的事實與數字依下列資料查證（2026 年 10 月）。
- Refraction, reflection, and dispersion in raindrops; about 42° (red 42.5° at 750 nm, 40.6° at 350 nm, water index 1.330–1.343); angle independent of drop size雨滴裡的折射、反射與色散；約 42°（750 nm 為 42.5°、350 nm 為 40.6°，折射率 1.330–1.343）；角度與雨滴大小無關Wikipedia, “Rainbow” ↗
- Red on the outside, violet on the inside; the center lies on the line from the Sun through your eye (the shadow of your head); a full circle from an airplane紅在外、紫在內；圓心在太陽穿過你眼睛的直線上（頭的影子）；從飛機上能看到整圈Wikipedia, “Rainbow” ↗
- Second rainbow at 50–53° with reversed colors; Alexander's band named for Alexander of Aphrodisias副虹 50–53°、顏色相反；亞歷山大暗帶以阿佛洛狄西亞的亞歷山大命名Wikipedia, “Rainbow” ↗
- Shen Kuo (Song dynasty) and al-Farisi (about 1300, water-filled glass sphere); Descartes (1637, large water-filled glass sphere)沈括（宋朝）與法里西（約 1300 年，裝水的玻璃球）；笛卡兒（1637 年，裝水的大玻璃球）Wikipedia, “Rainbow” (Scientific history) ↗
- Shen Kuo lived from 1031 to 1095沈括生於 1031 年、卒於 1095 年Wikipedia, “Shen Kuo” ↗
- Alexander of Aphrodisias lived around AD 200阿佛洛狄西亞的亞歷山大約活在公元 200 年Wikipedia, “Alexander of Aphrodisias” ↗