Lenses and the Lens Formula
How does a camera, a projector or a magnifying glass work? Slide the object past a convex or concave lensand see where the image forms, how big it is, and which way up.
Class 10 Refraction · Class 12 Ray OpticsTry this
0 of 5 doneBe a projector: make a real image bigger than the object.Hint: convex lens, object between 2F and F
Be a camera: make a real image smaller than the object.Hint: convex lens, object beyond 2F
Make a magnifying glass.Hint: convex lens, object inside F
Make a real image exactly the same size.Hint: object at 2F
Try a concave lens. What kind of image does it always make?Hint: switch to Concave lens
What's happening
Lenses bend light
Light slows down in glass, so it bends (refracts) as it goes in and out. A convex lens is thicker in the middle and bends rays together to a focus. A concave lens is thinner in the middle and spreads rays apart, as if they came from a focus in front of it.
Three easy rays
A ray parallel to the axis bends through the far focus F₂ (or, for a concave lens, appears to come from F₁). A ray through the optical centre goes straight on. A ray through F₁ comes out parallel. Where they meet is the image; if they only seem to meet when traced backwards, the image is virtual.
Power of a lens
Opticians describe lenses by their power in dioptres (D). A strong, short-focus lens has a big power. Convex lenses have positive power and correct long-sight; concave lenses have negative power and correct short-sight.
Who figured this out?
Hans Lipperhey
1608, NetherlandsA spectacle maker who applied for the first patent on a telescope: two lenses in a tube that made faraway things look nearer.
Johannes Kepler
1611, GermanyExplained how lenses form images and how the eye's lens focuses light on the retina, and designed a better telescope with two convex lenses.
Antonie van Leeuwenhoek
1670s, NetherlandsMade tiny, powerful single-lens microscopes and became the first person to see bacteria and other microbes.
Learn more
- Lens · Wikipedia
Check yourself
1. A convex lens has focal length 20 cm. What is its power?
2. Where must an object be for a convex lens to work as a magnifying glass?
3. The image formed by a concave lens is always…
4. An object is 30 cm from a convex lens of focal length 15 cm. Where is the image?
Common questions
How do you draw a ray diagram for a convex lens?
From the top of the object, draw a ray parallel to the principal axis: after the lens it passes through the second focus F₂. Draw a second ray through the optical centre: it goes straight on. A third ray through the first focus F₁ comes out parallel to the axis. The image is where these rays meet.
What is the lens formula?
1/v − 1/u = 1/f, where u is the object distance, v the image distance and f the focal length, measured from the optical centre with the New Cartesian sign convention. Magnification m = v/u = image height ÷ object height.
What is the power of a lens?
The power of a lens is the reciprocal of its focal length in metres: P = 1/f. Its unit is the dioptre (D). A convex lens of focal length 50 cm has power +2 D; a concave lens of focal length 25 cm has power −4 D.
What images does a convex lens form for different object positions?
Beyond 2F₁: real, inverted, diminished, between F₂ and 2F₂ (like a camera). At 2F₁: real, inverted, same size, at 2F₂. Between F₁ and 2F₁: real, inverted, magnified, beyond 2F₂ (like a projector). At F₁: image at infinity. Between F₁ and the lens: virtual, upright, magnified (a magnifying glass).
What is the difference between a convex and a concave lens?
A convex lens is thicker in the middle, converges light and can form real or virtual images; it is used in cameras, projectors, magnifiers and to correct long-sightedness. A concave lens is thinner in the middle, diverges light and always forms virtual, upright, diminished images; it is used to correct short-sightedness.
Which lens is used to correct myopia (short-sightedness)?
A concave lens of suitable power. It spreads the light slightly so that distant objects are focused on the retina instead of in front of it. Hypermetropia (long-sightedness) is corrected with a convex lens.
Thin lenses and paraxial rays, as in the Class 10 textbook. Real lenses also split colours slightly (chromatic aberration).
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