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Converging lenses

Waves, sound and light · level 7, lesson 2 of 6

A question to start

A magnifying glass can focus sunlight to a tiny bright spot. How does a curved piece of glass bring light together?

The idea

A converging (convex) lens is thicker in the middle. Rays parallel to its axis bend towards the axis and meet at the principal focus \(F\). The distance from the lens to \(F\) is the focal length \(f\). A fatter, more curved lens bends more and has a shorter focal length.

The power of a lens, in dioptres (D), is

\[P = \frac{1}{f}, \quad f \text{ in metres}.\]

To find an image, draw two rays from the top of the object:

  1. A ray parallel to the axis bends through \(F\) on the far side.
  2. A ray through the centre of the lens goes straight on.

Where they cross is the top of the image.

FFobjectimage

When the object is further than \(2f\) away, as here, the image is real (light really meets there), upside down and smaller. That is how a camera or an eye works. If the object is closer than \(f\), the rays never meet on the far side, and you see a virtual, upright, magnified image: a magnifying glass.

Worked examples

1. Power. A lens with \(f = 0.25\) m has \(P = 1/0.25 = 4\) D.

2. Focal length. A lens of power 10 D has \(f = 1/10 = 0.1\) m.

3. Burning spot. Sunlight arrives as parallel rays, so a magnifying glass focuses it at its focal point.

Try it

  1. What is the focal length of a lens?
  2. Find the power of a lens with a focal length of 50 cm.
  3. Which ray is easiest to draw through the centre of a lens, and why?
  4. Where must an object be for a converging lens to act as a magnifying glass?
Answers
  1. The distance from the lens to its principal focus.
  2. \(1/0.5 = 2\) D.
  3. The ray through the centre: it goes straight on, because the two faces there are almost parallel.
  4. Closer to the lens than its focal length.

Common mistake

"A real image is one you can see." A real image is one where light actually meets, so it can be caught on a screen. You can see a virtual image too, through the lens, but it cannot be caught on a screen.

Where it leads