Geometric Optics: Refraction, Lenses & Mirrors

The big idea

Light travels in straight lines until it meets a new material or a surface. At a boundary it bends (refraction) or bounces (reflection). Curved lenses and mirrors use these effects to form images, and three principal rays, or one equation, tell you where.

Key ideas

• Reflection: the angle of incidence equals the angle of reflection.
• Refraction: n₁ sin θ₁ = n₂ sin θ₂. Light bends toward the normal when it slows down (enters a higher n).
• Total internal reflection happens going from high n to low n, beyond the critical angle sin θ_c = n₂/n₁.
• The same equation, 1/d_o + 1/d_i = 1/f, works for lenses and mirrors. With the AP sign convention, a positive d_i means a real image.
• Converging lenses and concave mirrors (f > 0) form real, inverted images beyond F, and virtual, upright, enlarged images inside F. Diverging elements always form virtual, upright, reduced images.

Equations

Worked example

1. 1/d_i = 1/10 − 1/30 = 2/30 → d_i = +15 cm (real, on the far side).
2. m = −15/30 = −0.50: inverted and half size. This is how a camera works.
3. Object at 5.0 cm: 1/d_i = 1/10 − 1/5 = −1/10 → d_i = −10 cm (virtual, same side as the object).
4. m = −(−10)/5 = +2.0: upright and twice the size. This is a magnifying glass.

Common mistakes

• Dropping the sign of d_i and calling a virtual image real.
• Bending the light the wrong way at a boundary (toward the normal when entering a higher n).
• Thinking covering half a lens removes half the image. You still see the whole image, only dimmer.

Try it yourself

See it in action

Open the Ray Diagram Lab simulation and test every idea on this page yourself.

Open the simulation →