Diverging Lenses

A diverging lens curves the opposite way from a magnifying lens: thin in the center, thicker at the edges. Parallel rays hitting it bend away from the center line instead of toward it, so they never meet on the far side. Trace them backward, though, and they all seem to come from one point on the same side as the object. That point is the focal point, but because the rays only appear to come from it, the focal length is written as negative, and the image is called virtual.

To locate the image, draw two of the three standard rays. One ray travels parallel to the axis, then bends as if coming from the near focal point. A second ray heads straight toward the far focal point but exits parallel to the axis. A third goes straight through the center of the lens, undeflected. All three, extended backward, cross at the same point on the object's side of the lens: that crossing is the virtual image, always upright and smaller than the object. The thin lens equation 1/f = 1/do + 1/di still works here, as long as f is negative.

This sits opposite the converging lens in the unit: converging lenses can make real or virtual images depending on object distance, but a diverging lens only ever makes one kind of image, no matter where the object sits. That single, predictable outcome is exactly why nearsighted corrective lenses are diverging: they shrink and spread the image so it focuses correctly in an eye that over-converges light.