A lens bends light twice, once at each surface, by Snell's Law. A converging lens is thicker in the middle and brings parallel rays together at a focal point on the far side. A diverging lens is thinner in the middle and spreads parallel rays as if they came from a focal point on the near side. Ray diagrams work just as for mirrors, but the light goes through.
Why it works
Why does a thick-middled lens converge light? Near its edge, a lens is like a thin prism with its thick end toward the middle. A prism bends light toward its thicker part, so every part of the lens bends light toward the axis, and the edges, which are more steeply tilted, bend it most. That is just what it takes to bring parallel rays to one point.
Key idea
Principal rays for a lens: (1) parallel to the axis, then through the far focal point (converging) or as if from the near one (diverging); (2) straight through the center, undeflected; (3) through the near focal point (converging) or aimed at the far one (diverging), then out parallel. Real images form on the far side of the lens.
| Object (converging lens) | Image | Use |
|---|---|---|
| beyond $2f$ | real, inverted, smaller | camera, eye |
| between $f$ and $2f$ | real, inverted, larger | projector |
| inside $f$ | virtual, upright, larger | magnifying glass |
Common mistake
Thinking that blocking half of a lens cuts off half of the image. Every point of the object sends light through the whole lens, so the open half still makes a complete image with half the light. Check: a camera with a smaller aperture still takes a whole picture, only a darker one.
Worked example: A camera lens
A camera lens has $f = 5.0\ \text{cm}$. Where is the image of a person $3.0\ \text{m}$ away, and what is it like?
- The person is far beyond $2f = 10\ \text{cm}$.
- The parallel ray and the center ray meet just beyond $F$ on the far side.
- Real, inverted and much smaller, just past $5.0\ \text{cm}$: right where the sensor sits.
Answer: Real, inverted, smaller, just beyond F
Worked example: A magnifying glass
You hold a converging lens with $f = 10\ \text{cm}$ $6\ \text{cm}$ above a stamp. What do you see?
- The stamp is inside $f$.
- Rays leaving the lens spread apart; traced back, they meet on the stamp's side, farther away.
- A virtual, upright, enlarged image: that is what a magnifier does.
Answer: Virtual, upright, larger