An object is 30cm from a converging lens with f=10cm. Where is the image?

1/f = 1/d_o + 1/d_i → 1/d_i = 1/10 − 1/30 = 2/30 → d_i = 15cm.

What is the magnification for the setup above?

M = −d_i/d_o = −15/30 = −0.5 (inverted, smaller).

Why does a magnifying glass work? (d_o < f).

When d_o < f, the lens equation gives d_i < 0: a virtual upright image appears on the same side.

Pro 🔒~20 min

Geometric Optics: Basics

Q: Why does a magnifying glass work? (d_o < f).

When d_o < f, the lens equation gives d_i < 0: a virtual upright image appears on the same side.

Explore how lenses and mirrors form images

How it works

Geometric Optics: Basics demonstrates a key principle: Converging (convex) lenses bend light rays toward the focal point. Converging (convex) lenses bend light rays toward the focal point. The thin lens equation relates object distance d_o, image distance d_i, and focal length f. When d_o > f, a real, inverted image forms; when d_o < f, a virtual, upright image appears (magnifying glass). Diverging (concave) lenses always form virtual, diminished, upright images. Mirrors follow the same mathematics with light traveling on one side.

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Step-by-step

Drag the object (arrow) along the principal axis.
Rays automatically trace through the lens.
Toggle between converging/diverging lens and concave/convex mirror.
Observe how image position and orientation change as object crosses the focal point.

Key formulas

$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$ Thin lens equation
$m = -\frac{d_i}{d_o}$ Magnification
$P = \frac{1}{f}$ Lens power (diopters)

Frequently asked questions

An object is 30cm from a converging lens with f=10cm. Where is the image?: 1/f = 1/d_o + 1/d_i → 1/d_i = 1/10 − 1/30 = 2/30 → d_i = 15cm.
What is the magnification for the setup above?: M = −d_i/d_o = −15/30 = −0.5 (inverted, smaller).
Why does a magnifying glass work? (d_o < f).: When d_o < f, the lens equation gives d_i < 0: a virtual upright image appears on the same side.