← Optics

Convex Lens

Drag the object towards the lens and watch where its image appears.

2FFF2FReal imageObject

Upside down and smaller, on the far side, where a screen could catch it. Like a camera or your eye, looking at something far away.

Object distance
26 cm
Image distance
16.3 cm behind the lens
Size
0.6 × upside down

What’s happening

A convex lens is thicker in the middle. It bends light inwards, so rays from the tip of the object meet again on the far side and make an upside-down picture you could catch on a screen. Bring the object closer than the focus F and the rays spread apart instead: they never meet, but your eye traces them back to a bigger, upright image. That is how a magnifying glass works.

Try this

  • Start far away, then slowly bring the object closer. When does the image get bigger than the object?
  • Put the object exactly on 2F. How big is the image?
  • Cross the focus F. What happens to the image?
  • Make the lens fatter (a shorter focal length). Where does the image go?
  • At home: put a drop of water on a clear plastic sheet lying on a newspaper. The drop is a tiny convex lens. What does it do to the letters?
Learn more: the three rays and the lens equation

Any two of these three rays are enough to find the image:

  • Parallel ray: comes in parallel to the axis, and leaves through the far focus.
  • Centre ray: goes straight through the middle of the lens without bending.
  • Focal ray: goes through the near focus, and leaves parallel to the axis.

The lens equation links the three distances, where uu is the object distance, vv the image distance and ff the focal length:

1f=1u+1v\frac{1}{f} = \frac{1}{u} + \frac{1}{v}

The image is mm times as big as the object; a minus sign means upside down:

m=−vum = -\frac{v}{u}
  • Beyond 2F: smaller and upside down (a camera).
  • At 2F: the same size, upside down (a photocopier at 1:1).
  • Between F and 2F: bigger and upside down (a projector).
  • At F: no image; the light leaves in a parallel beam (a spotlight).
  • Inside F: bigger and upright, on the same side (a magnifying glass).

See it at Science Playground