How do I find the object distance from the image distance?

Rearrange the thin lens equation: 1/u = 1/f − 1/v. A converging lens with f = 10 cm makes a real image at v = 30 cm, so 1/u = 1/10 − 1/30 = 2/30 and u = 15 cm, with m = −30/15 = −2. Pick Object distance u under Solve for to see each step and move the sim there.

How do you draw a ray diagram for a convex lens?

From the top of the object draw a ray parallel to the axis that bends through the far focal point F, and a ray straight through the centre of the lens. Where they cross is the top of the image. A third ray through the near focal point, which leaves parallel to the axis, is a good check.

When does a converging lens make a virtual image?

When the object is closer to the lens than the focal length. The rays leave the lens spreading out, so they never meet; traced backwards they seem to come from an upright, magnified image on the object's side. That is how a magnifying glass works.

What happens when the object is at 2F?

The image forms at 2F on the other side, real, inverted and exactly the same size: v = u = 2f and the magnification is 1.

Why does a diverging lens always give a virtual image?

It spreads every ray out, so rays from a real object never meet after the lens. Their backward extensions meet between the lens and the near focal point, giving an upright, diminished, virtual image wherever the object is.

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Lenses and ray diagrams

A lens bends light so that rays from one point of an object meet again at one point of an image. Move the object and the image moves, grows, shrinks or flips.

Just need the number? Physics Formulas

Image distance v against object distance u

Readouts

What's happening

A converging (convex) lens bends parallel rays inwards so they meet at the principal focus F, a focal length f from the lens. A diverging (concave) lens spreads parallel rays out as if they came from a focus on the near side. To find an image you only need two of three rays from the top of the object: one through the centre of the lens, which goes straight on; one parallel to the axis, which leaves through F; and one through F on the near side, which leaves parallel. Where the rays really meet there is a real image you could catch on a screen, and it is upside down. If the rays leaving the lens spread apart, you trace them back with dashed lines: they seem to come from a virtual image, which is upright and on the same side as the object. Inside the focal length a converging lens works as a magnifying glass. The thin lens equation gives the same answer as the drawing.

1/f = 1/u + 1/vmagnification = image height / object height = v / uP = 1/f (f in m)

GCSE Physics (AQA, Edexcel, OCR): lenses, ray diagrams, real and virtual images and magnification. A-Level Physics (OCR, WJEC): the thin lens equation and lens power.

Challenge

Predict first: a converging lens has f = 10 cm and the object stands 15 cm away. How far behind the lens does the image form, and is it bigger or smaller than the object? Set it up and check.

FAQ

How do I find the object distance from the image distance?: Rearrange the thin lens equation: 1/u = 1/f − 1/v. A converging lens with f = 10 cm makes a real image at v = 30 cm, so 1/u = 1/10 − 1/30 = 2/30 and u = 15 cm, with m = −30/15 = −2. Pick Object distance u under Solve for to see each step and move the sim there.
How do you draw a ray diagram for a convex lens?: From the top of the object draw a ray parallel to the axis that bends through the far focal point F, and a ray straight through the centre of the lens. Where they cross is the top of the image. A third ray through the near focal point, which leaves parallel to the axis, is a good check.
When does a converging lens make a virtual image?: When the object is closer to the lens than the focal length. The rays leave the lens spreading out, so they never meet; traced backwards they seem to come from an upright, magnified image on the object's side. That is how a magnifying glass works.
What happens when the object is at 2F?: The image forms at 2F on the other side, real, inverted and exactly the same size: v = u = 2f and the magnification is 1.
Why does a diverging lens always give a virtual image?: It spreads every ray out, so rays from a real object never meet after the lens. Their backward extensions meet between the lens and the near focal point, giving an upright, diminished, virtual image wherever the object is.