Images Formed by Lenses · 透镜形成的像
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| lens/lenz/ | 透镜 | tòu jìng |
A magnifying glass, a camera, your own eye
- Hold a magnifying glass over a page and the letters swell; a camera shrinks a whole scene onto a sensor.
- Both use a lens 透镜, a shaped piece of glass that bends light by refraction.
- By bending rays to meet, a lens builds an image of whatever it looks at.
- Two simple rays are all you need to find where that image sits.
放大镜、相机、你自己的眼睛
- 把放大镜举在书页上,字母变大;相机把整个场景缩到传感器上。
- 两者都用透镜,一块经过塑形的玻璃,靠折射弯折光。
- 透镜通过弯折光线使之相会,构建出它所看之物的像。
- 只需两条简单的光线,就能找到那个像的位置。
Converging and diverging lenses
- A converging (convex) lens is thicker in the middle; it bends parallel rays together to a focus.
- A diverging (concave) lens is thinner in the middle; it spreads parallel rays apart.
- The focal length $f$ is the distance from the lens to its focal point.
- A converging lens is the workhorse of cameras, projectors and the human eye.
会聚透镜与发散透镜
- 会聚(凸)透镜中间较厚;它把平行光线弯到一起聚成焦点。
- 发散(凹)透镜中间较薄;它把平行光线分开。
- 焦距 $f$ 是从透镜到它焦点的距离。
- 会聚透镜是相机、投影仪和人眼的主力。
A converging (convex) lens is: · 会聚（凸）透镜是：
A converging lens is thicker in the middle and bends parallel rays to a focus. · 会聚透镜中间较厚，能将平行光线会聚于一点。
Drawing the ray diagram
- Ray 1: from the top of the object, parallel to the axis, then bent through the far focus.
- Ray 2: from the top of the object, straight through the centre of the lens (undeviated).
- Where the two rays cross is the top of the image.
- Beyond the focal point the image is real and inverted; inside it, virtual and upright (a magnifier).
画光路图
- 光线 1:从物顶发出,平行于轴,然后经远焦点弯折。
- 光线 2:从物顶发出,直穿透镜中心(不偏折)。
- 两条光线相交处就是像的顶端。
- 焦点之外,像是实的、倒立的;焦点之内,是虚的、正立的(放大镜)。
Build the lens image · 构建透镜成像
Move the object nearer and farther than the focal point and watch the image switch from real to virtual. · 将物体移至焦点前后，观察图像在实像与虚像之间切换。
An object beyond the focal length of a converging lens forms an image that is: · 当物体位于凸透镜焦距之外时，所成的像是：
Beyond $f$, the rays cross to form a real, inverted image. · 在 $f$ 之外，光线交叉形成倒立的实像。
Select all · 所有 correct statements about lenses. · 选择关于透镜的所有正确陈述。
Converging lenses focus rays (the diverging one spreads them); the centre ray is undeviated; inside f gives a magnifier. · 会聚透镜使光线会聚（发散透镜使其散开）；过光心光线不偏折；物体在 f 以内起放大镜作用。
The lens equation
- Object distance $u$, image distance $v$ and focal length $f$ obey $\dfrac{1}{f} = \dfrac{1}{u} + \dfrac{1}{v}$.
- Solve it to find exactly where the image forms and how big it is.
- The magnification is the ratio of image to object height (or $v/u$).
- Camera and eye both move the lens or change $f$ to keep the image sharp.
透镜方程
- 物距 $u$、像距 $v$ 和焦距 $f$ 遵守 $\dfrac{1}{f} = \dfrac{1}{u} + \dfrac{1}{v}$。
- 解它就能精确求出像在哪里、有多大。
- 放大率是像高与物高之比(或 $v/u$)。
- 相机和眼睛都靠移动透镜或改变 $f$ 来保持像清晰。
An object is $6\ \text{cm}$ from a converging lens of $f = 2\ \text{cm}$. What is the image distance $v$, in cm? · 一个物体位于距 $6\ \text{cm}$ 为 $f = 2\ \text{cm}$ 的凸透镜前。求像距 $v$，单位为 cm？
$1/v = 1/2 - 1/6 = 2/6 \Rightarrow v = 3\ \text{cm}$.
The lens equation is $\dfrac{1}{f} = \dfrac{1}{u} + \dfrac{1}{\_\_}$ (fill in the symbol). · 透镜公式为 $\dfrac{1}{f} = \dfrac{1}{u} + \dfrac{1}{\_\_}$（填入符号）。
$1/f = 1/u + 1/v$ — object, image and focal distances. · $1/f = 1/u + 1/v$ —— 物距、像距和焦距。
A converging lens does not always give a real, inverted image. When the object is inside the focal length, the image is virtual, upright and magnified — that is exactly how a magnifying glass works. The object must be beyond $f$ to get a real, inverted image.
会聚透镜并不总是给出实的、倒立的像。当物体在焦距以内时,像是虚的、正立的、放大的——这正是放大镜的工作方式。物体必须在 $f$ 之外才能得到实的、倒立的像。
A converging lens used as a magnifying glass has the object inside the focal length, giving a virtual, upright, magnified image. · 用作放大镜的凸透镜，物体位于焦距之内，形成正立、放大的虚像。
Inside · 内部 $f$, the image is virtual, upright and enlarged — the magnifier case. · 在 $f$ 之内，像为虚像、正立且放大——即放大镜的情形。
An object is $6\ \text{cm}$ from a converging lens of focal length $f = 2\ \text{cm}$. Find the image distance $v$.
- $\dfrac{1}{v} = \dfrac{1}{f} - \dfrac{1}{u} = \dfrac{1}{2} - \dfrac{1}{6} = \dfrac{3-1}{6} = \dfrac{2}{6}$.
- $v = 3\ \text{cm}$ — a real, inverted image on the far side.
一个物体距一个焦距 $f = 2\ \text{cm}$ 的会聚透镜 $6\ \text{cm}$。求像距 $v$。
- $\dfrac{1}{v} = \dfrac{1}{f} - \dfrac{1}{u} = \dfrac{1}{2} - \dfrac{1}{6} = \dfrac{3-1}{6} = \dfrac{2}{6}$。
- $v = 3\ \text{cm}$——在另一侧的实、倒立像。
A converging lens bends parallel rays to a focus and forms an image; use the parallel ray and the centre ray to find it. Beyond $f$ the image is real and inverted; inside $f$ it is virtual, upright and magnified. The lens equation $\dfrac1f = \dfrac1u + \dfrac1v$ locates it.
会聚透镜把平行光线弯到焦点并成像;用平行光线和中心光线找到它。$f$ 之外像是实的、倒立的;$f$ 之内是虚的、正立的、放大的。透镜方程 $\dfrac1f = \dfrac1u + \dfrac1v$ 定位它。