Lenses and dispersion
Introduced| English | Meaning |
|---|---|
| dispersion/dɪˈspɜːʃn/ | The splitting of white light into different colours because each colour refracts by a different amount. |
| diverging lens/daɪˈvɜːdʒɪŋ lenz/ | A lens that spreads parallel rays apart as if they came from a virtual focus; thinner in the middle. |
| converging lens/kənˈvɜːdʒɪŋ lenz/ | A lens that brings rays parallel to its principal axis together at a real principal focus. |
| principal focus/ˈprɪnsɪpl ˈfəʊkəs/ | The point where rays parallel to the principal axis meet, or appear to diverge from, after passing through a lens. |
| focal length/ˈfəʊkl leŋθ/ | The distance from the centre of a lens to its principal focus. |
| real image/rɪəl ˈɪmɪdʒ/ | An image formed where light rays actually converge, which can be projected onto a screen. |
| virtual image/ˈvɜːtʃuːəl ˈɪmɪdʒ/ | An image formed where light rays appear to come from, without actually converging there. |
| spectrum/ˈspektrəm/ | A distribution of electromagnetic radiation according to wavelength or frequency. |
| monochromatic/ˌmɒnəʊkrəʊˈmætɪk/ | Consisting of a single frequency or a very narrow range of frequencies of light or other radiation. |
Focusing and splitting light
- A magnifying glass makes tiny print big; a prism turns white light into a rainbow.
- Both use refraction — bending light in a careful, shaped way.
- Meet the lens and dispersion 色散.
Converging and diverging lenses 凹透镜
- A converging lens 凸透镜 is fat in the middle. It bends parallel rays inwards to meet at the principal focus 焦点.
- The distance from the lens to that focus is the focal length 焦距 $f$.
- A diverging lens is thin in the middle and spreads rays out.
A converging lens and its principal focus
Image formation by a converging lens
Trace the three special rays from the object — where they meet is the image. Move the object closer than the focal point to flip it into a magnifying glass.
A converging lens makes parallel rays of light:
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A converging (convex) lens bends parallel rays inward so they meet at the principal focus.
The distance from the lens to its principal focus is called the ____ length.
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The focal length is the distance from the centre of the lens to the principal focus.
Images from a lens
- A converging lens can make a real image 实像 — the rays really meet, so it can be shown on a screen (as in a camera or the eye).
- When the object is very close, it makes a larger virtual image 虚像 instead.
- Used close to the eye like this, the lens is a magnifying glass.
Used close to the eye as a magnifying glass, a converging lens makes a:
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With the object very close, the lens forms an enlarged, upright virtual image — a magnifying glass.
Dispersion
- A glass prism splits white light into a band of colours — the spectrum 光谱. This splitting is dispersion.
- The order is red, orange, yellow, green, blue, indigo, violet.
- Red bends least: it has the longest wavelength and lowest frequency. Violet is the opposite.
- Light of a single colour (one frequency) is monochromatic 单色.
Put these spectrum colours in order of wavelength, longest first.
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Red has the longest wavelength and violet the shortest, so: red, yellow, green, blue, violet.
Which colour of visible light has the longest wavelength?
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Red light has the longest wavelength and lowest frequency; violet has the shortest wavelength and highest frequency.
Worked examples
1. Lens $f = 3.0\ \text{cm}$, object $2.0\ \text{cm}$ tall and $9.0\ \text{cm}$ away (left). The two rays meet $4.5\ \text{cm}$ behind the lens: the image is real, inverted, diminished ($1.0\ \text{cm}$ tall).
2. Same lens, object $1.0\ \text{cm}$ tall and $2.0\ \text{cm}$ away (right). The rays spread apart; traced back they meet $6.0\ \text{cm}$ in front of the lens: the image is virtual, upright, enlarged ($3.0\ \text{cm}$ tall) — a magnifying glass.
Real or virtual is about the rays, not the size. A real image is where rays really meet, so a screen can show it. A virtual image is where rays only seem to come from.
You've got it
- a converging lens brings parallel rays to the principal focus; lens-to-focus = focal length
- it makes a real image (on a screen) — or a magnified virtual image when the object is close (magnifying glass)
- a prism causes dispersion: white light → red…violet
- red = longest wavelength, lowest frequency; violet = shortest, highest
Write from a focal length of 15 cm
- A converging lens has a focal length of 15 cm. An object is placed 8 cm from the lens.
- Say where a distant object is imaged, and what kind of image the close object gives.
A converging lens has focal length 15 cm. Where does a distant object form its image, and what kind of image does an object 8 cm from the lens give?
The focal length is the lens-to-focus distance for parallel rays. Inside that distance the lens is a magnifying glass.
Where is the image of a distant object?
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Parallel rays from a distant object meet at the principal focus, 15 cm from the lens.