🎓 Prepared by students from Boğaziçi University

What are Lenses?

A lens is a curved piece of transparent material that bends light to form an image. Converging lenses focus light to a point, while diverging lenses spread it out — together they underpin cameras, eyeglasses, microscopes and telescopes.

Short answer

A lens refracts light at two curved surfaces to form an image; the thin lens equation 1/f = 1/do + 1/di relates focal length, object distance and image distance.

How a Converging Lens Forms an Image

1
Ray parallel to the axis
Refracts through the far focal point
↓
2
Ray through the center
Passes straight through undeviated
↓
3
Ray through the near focal point
Emerges parallel to the axis
↓
4
Rays converge
Where they meet marks the real image

Try it: interactive calculator

Image distance di

15cm

= (10*30)/(30-10)

Focal length f10 cmObject distance do30 cm

Step-by-step worked examples

An object sits 30 cm from a converging lens with f = 10 cm. Find the image distance.

di = f·do/(do−f)
di = (10×30)/(30−10) = 300/20
di = 15 cm (real image)

An object sits 5 cm from the same lens (f = 10 cm), inside the focal length. Find the image.

di = (10×5)/(5−10) = 50/−5
di = −10 cm → virtual, upright, magnified image (like a magnifying glass)

An object is 20 cm from a diverging lens with f = −15 cm. Find the image distance.

di = (−15×20)/(20−(−15)) = −300/35
di ≈ −8.6 cm → virtual, reduced image

Flashcards

Quick quiz

Q1.Which lens is thicker at the center than the edges?

Correct answer: B. Converging (convex) lenses bulge outward and are thickest at the center.

Q2.An object placed inside a converging lens's focal length produces…

Correct answer: B. Inside f, the lens acts like a magnifying glass — image is virtual, upright and enlarged.

Q3.For f = 10 cm and do = 30 cm, what is di?

Correct answer: B. di = (10×30)/(30−10) = 15 cm.

Q4.A diverging lens always produces…

Correct answer: B. Diverging lenses only ever form virtual, upright, reduced images.

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Common mistakes

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Assuming every lens forms a real image. — Correct: A converging lens forms a virtual image when the object is inside the focal length; diverging lenses always form virtual images.

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Mixing up which lens is converging and which is diverging by name only. — Correct: Look at the shape: convex (thicker at center) converges, concave (thinner at center) diverges.

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Forgetting the sign convention for diverging lenses (f is negative). — Correct: Diverging lens focal lengths are taken as negative in 1/f = 1/do + 1/di.

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Ignoring the magnification sign. — Correct: Negative m means the image is inverted; positive m means upright.

FAQ

What is a lens?

A lens is a transparent optical device with curved surfaces that refracts light to form an image, used in glasses, cameras and microscopes.

What is the lens formula?

1/f = 1/do + 1/di, relating focal length, object distance and image distance.

What are examples of lenses?

Eyeglasses, camera lenses, magnifying glasses, microscope objectives and telescope lenses.

How do you calculate image distance for a lens?

Rearrange the lens formula: di = f·do/(do−f), using the known focal length and object distance.