Short on time? This page is the recap. For the ray diagrams, the sᵢ–sₒ sketch and the worked examples, use the full study guide.
Recap
- Converging lens (thicker in the middle): parallel rays meet at F on the transmitted side.
- Diverging lens (thinner in the middle): parallel rays spread as if from F on the incident side.
- A thin lens has a focal point on each side, both a distance f from the lens when the same medium surrounds it.
- Real image: refracted rays actually meet; can be shown on a screen. Virtual image: rays only appear to come from a point.
- Principal rays: (1) parallel, then through or away from F; (2) straight through the centre; (3) through or toward F, then parallel.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| 1/sᵢ + 1/sₒ = 1/f | all distances in the same unit, measured from the lens midline | find the image position, the object position or f |
| |M| = |hᵢ/hₒ| = |sᵢ/sₒ| | size ratio: no units, no sign | find image height; decide enlarged or reduced |
| single lens: real image ⇒ inverted, virtual image ⇒ upright | sᵢ > 0 real, sᵢ < 0 virtual | state the orientation in words |
| 1/sᵢ = −1/sₒ + 1/f | graph 1/sᵢ against 1/sₒ: slope −1, intercepts 1/f | find f from data |
| Lens and object | Image |
|---|---|
| Converging, sₒ > 2f | real, inverted, reduced |
| Converging, sₒ = 2f | real, inverted, same size |
| Converging, f < sₒ < 2f | real, inverted, enlarged |
| Converging, sₒ = f | no image (rays leave parallel) |
| Converging, sₒ < f | virtual, upright, enlarged |
| Diverging, any sₒ | virtual, upright, reduced |
Assumptions behind the numbers
- The lens is thin: rays bend once, at the midline.
- Rays stay close to the principal axis, so all parallel rays meet at one focal point.
- The object is real (sₒ > 0) and the same medium surrounds the lens.
Mistakes to avoid
- Positive f for a diverging lens. It must be negative.
- 1/sᵢ = 1/f + 1/sₒ. Subtract: 1/sᵢ = 1/f − 1/sₒ.
- Forgetting to take the reciprocal at the end.
- Calling a virtual image “imaginary” or “not there”. You can see it through the lens.
- Half a lens, half an image. The full image forms, dimmer.
- Giving |M| a sign. Quote the size ratio and say “upright” or “inverted” in words.
Quick self-check
- f = 20 cm, sₒ = 25 cm. Where is the image, and what is |M|? (sᵢ = +100 cm; |M| = 4.0, real and inverted)
- A diverging lens has f = −10 cm and the object is 10 cm away. Find sᵢ and |M|. (sᵢ = −5.0 cm; |M| = 0.50, virtual and upright)
- Where must an object be for a converging lens to form a same-size image? (At 2f)
Next: practice questions.