A little room to wonder

Refraction & Lenses

Trace an ideal light ray across a boundary and explain why angles must be measured from the normal.

What changes when light enters a different transparent material?

A museum animation device shows successive horse-and-rider images reflected around a circular arrangement.
The approved praxinoscope uses mirrors to view successive animation images. It offers a comparison with reflection, rather than depicting the article’s refracting boundary or a lens specification.User:FA2010 · Source · Public domain

Begin with a boundary and a normal

Refraction concerns light passing between media with different refractive indices. In the simple transparent-medium model, speed is c/n, where c is the vacuum speed and n is refractive index. A change of speed can accompany a change of ray direction at a boundary. At normal incidence the ray does not bend sideways.

Draw a normal: a line perpendicular to the boundary at the crossing point. Incident and refracted angles are measured from that line, not from the surface. Some light can also be reflected. A transmitted-ray model follows one part of what happens rather than claiming every incoming ray passes through.

Worked example: an ideal air-to-glass ray

Take an idealised boundary with air index 1.0 and glass index 1.5. Let the incoming ray make 30° with the normal. Snell’s law is n₁ × sin(angle₁) = n₂ × sin(angle₂). Since sin(30°) = 0.5, the transmitted angle must have sine 0.5/1.5 = 1/3.

That gives an angle of approximately 19.5° from the normal, so the transmitted ray is closer to the normal. The glass value is a supplied model value, not a measurement of every glass. If you measure from the surface instead, you will draw the wrong angle even with correct arithmetic.

Connect a boundary to a lens

A lens has shaped boundaries that redirect rays in a coordinated way. In an ideal thin converging-lens model, incoming rays parallel and close to the optical axis meet at a focal point. A diverging lens makes those rays spread as though coming from a point on the incoming side.

These are approximations, not a guarantee that any curved transparent object forms a perfect image. Real lenses have thickness, different surfaces and imperfections. The surrounding medium also matters. A paper ray diagram can explain the model without using a lens or producing a beam.

Keep the model and activity safe

Label which medium each ray segment occupies, put arrows on the direction of travel, and distinguish the normal from the lens axis. A single flat-boundary normal and a whole lens’s optical axis are related drawing tools but are not interchangeable labels.

Use only the supplied diagram instructions and fictional indices. No sunlight, laser, bright light source, optical equipment or real viewing task is needed. The goal is to explain a model’s angles and assumptions, rather than to focus light or judge an instrument’s performance.

Only if you feel like trying

Trace an ideal ray on paper

  1. Draw the supplied flat boundary, normal and a 30° incoming ray.
  2. Mark the transmitted ray approximately 19.5° from the normal in the index-1.5 medium.
  3. Describe how a converging-lens model combines shaped boundaries, and list one approximation.

Optional. Use paper or talk through the supplied fictional example. No purchase, personal information, account, public sharing or practical experiment is needed.