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Thin lens formula Formula, SPM Physics

Formula: 1/f = 1/u + 1/v. Not given in the exam, recall it.

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Thin lens formula
1/f = 1/u + 1/v

Not given in the exam, recall it.

What it is for

Thin lens formula is used in Light and Optics (SPM Physics Form 4). Keep the SI units in every line of working. Light and Optics

Symbols and SI units

SymbolMeaningSI unit
ffocal lengthm
uobject distancem
vimage distancem

Rearrangements

  • 1/u = 1/f − 1/v
  • 1/v = 1/f − 1/u
  • f = uv / (u + v)

Worked example

A convex lens forms a real image: u = 20 cm, v = 30 cm. 1/f = 1/u + 1/v = 1/20 + 1/30 = 5/60 = 1/12, so f = 12 cm.

Common trap

Apply the sign convention (real distances +, virtual −). Take the reciprocal at the end to get f, not 1/f.

Understanding the thin lens formula

The thin lens formula 1/f = 1/u + 1/v relates three distances measured along the principal axis. f is the focal length, u the object distance, and v the image distance, all in metres (m) in SI, though centimetres are common in questions as long as you stay consistent.

The reciprocals add because each surface contributes a share of the bending. A stronger lens (short f) can form an image with a shorter u or v.

To find any one unknown, rearrange: 1/v = 1/f − 1/u, or 1/u = 1/f − 1/v, or combine into f = uv / (u + v). Always work in reciprocals first, then invert the final answer, a step students often forget.

A worked example, step by step

A convex lens has focal length f = 10 cm. An object is placed at u = 15 cm.

Where is the image?

Rearrange for the image distance:

  • 1/v = 1/f − 1/u = 1/10 − 1/15
  • 1/v = 3/30 − 2/30 = 1/30 cm⁻¹
  • v = 30 cm

The image forms v = 30 cm on the far side of the lens (2 significant figures). Because v is positive, the image is real and can be caught on a screen.

Check with the combined form: f = uv/(u+v) = (15 × 30)/(15 + 30) = 450/45 = 10 cm, matching the given focal length.

Common mistakes and how this is tested

The key trap: apply the sign convention (real distances +, virtual −) and take the reciprocal at the end to get f, not 1/f.

Other common errors:

  • Adding 1/u and 1/v as ordinary numbers, e.g. writing 1/20 + 1/30 = 1/50.
  • Mixing centimetres and metres within one calculation.
  • Forgetting to invert, leaving the answer as 1/12 instead of 12.

You will be asked to calculate f, u or v, to define focal length, or to explain whether the image is real or virtual based on the sign of v.

Source: DSKP KSSM Physics Form 4 and 5 (Versi English), Sijil Pelajaran Malaysia: Format Pentaksiran mulai 2021, Fizik (4531) (Bahagian Pembangunan Kurikulum (BPK), KPM)

Written by the spmphysics.com.my editorial team.· Updated 5 Sept 2026

Frequently asked questions

Is this formula given in the exam?
No. SPM Physics papers provide no formula sheet, so this must be recalled.
What does a negative image distance mean?
A negative v means the image is virtual, it forms on the same side as the object and cannot be projected onto a screen, as with a magnifying glass held close to an object.
Can I keep everything in centimetres?
Yes. The formula works in any single unit provided f, u and v all use it. The SI unit is the metre, but centimetres are fine as long as you do not mix them.
Why do the reciprocals add rather than the distances?
The lens equation comes from how each refracting surface bends light. The bending powers combine, and power is inversely proportional to distance, so the reciprocals add.

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