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
| Symbol | Meaning | SI unit |
|---|---|---|
| f | focal length | m |
| u | object distance | m |
| v | image distance | m |
Rearrangements
1/u = 1/f − 1/v1/v = 1/f − 1/uf = uv / (u + v)
Worked example
Common trap
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)