The lens formula gives the image distance for a given object distance and focal length. The magnification then tells you how large the image is compared with the object.
This lesson is part of SPM Physics light and optics. Always sketch the diagram from drawing ray diagrams for lenses first, so you can tell whether your answer makes sense.
What are the formulae?
Use the real-is-positive convention.
- Lens formula: 1/f = 1/u + 1/v, so 1/v = 1/f − 1/u.
- Magnification: m = v ÷ u, using the size of the value.
- Image height = m × object height.
Worked example 1: a real image
An original question: a convex lens has f = 12 cm. An object 6.0 cm tall is 30 cm from the lens. Find v, m and the image height.
1/v = 1/12 − 1/30 = 5/60 − 2/60 = 3/60 = 1/20, so v = 20 cm.
m = 20 ÷ 30 = 0.67, and the image height is 0.67 × 6.0 = 4.0 cm.
v is positive, so the image is real. The object is beyond 2F (2F is 24 cm), so the diagram predicts a real, inverted, diminished image between F and 2F, and 20 cm agrees.
Worked example 2: a virtual image
A convex lens has f = 10 cm and an object is 6 cm from the lens.
1/v = 1/10 − 1/6 = 3/30 − 5/30 = −2/30 = −1/15, so v = −15 cm.
m = 15 ÷ 6 = 2.5. The negative v means the image is virtual, upright and magnified, on the same side as the object.
The mistake that costs marks
The common slip is to subtract the distances before taking the reciprocal, for example 1/v = 1/(12 − 30). The formula adds reciprocals, so invert each distance first.
| Step | Wrong | Right |
|---|---|---|
| Write 1/v | 1/(12 − 30) = −1/18 | 1/12 − 1/30 |
| Combine | v = −18 cm | 3/60, so v = 20 cm |
Another slip is to stop at 1/v. Take the final reciprocal to get v, and then check the sign against your diagram.
Check yourself
A convex lens has f = 15 cm. An object 2.0 cm tall is placed 20 cm from the lens. Find the image distance, magnification and image height.
Answer
1/v = 1/15 − 1/20 = 4/60 − 3/60 = 1/60, so v = 60 cm.
m = 60 ÷ 20 = 3, so the image height is 3 × 2.0 = 6.0 cm.
The object is between F and 2F (15 cm to 30 cm), so the image should be real, inverted and magnified, beyond 2F. A value of 60 cm agrees.
What to study next
Use the calculation alongside diagrams in explaining optical-instrument principles. Then test yourself with the light and optics practice set.
The units and significant-figure checker helps you present answers correctly. If you want a teacher to review your calculation steps, see online one-to-one Physics tuition.