At the boundary of two worlds

When does light bend, and when can it not escape?

When does light bend, and when can it not escape?

1. Set n₁=1 and n₂=1.5, then increase incidence.
2. Swap the indices and look for the critical angle.
3. Compare with equal-index media.

What to measure

n is refractive index; c/n is phase speed; angles are to the normal.

The idea underneath

A wave changes speed when it crosses media with different refractive indices. Continuity of phase along the interface gives Snell’s law. Entering a higher-index medium bends a ray toward the normal. From higher to lower index, an angle can be reached beyond which no propagating transmitted ray exists: total internal reflection. The laboratory explicitly reports this state rather than drawing an impossible refracted ray.

Build the argument

1. Identify the optical axis and the normal to each interface.
2. Apply reflection, Snell’s law, or the paraxial lens equation according to the model.
3. Check limiting cases: equal indices, object at the focal plane, or a slit much wider than the wavelength.

Worked example 1

At 30° from air to n=1.5, θ₂=19.47°.

Worked example 2

For n₁=1.5 to n₂=1, θc=41.81°.

Applications

Cameras, microscopes and fibre links combine geometric paths with wave limitations. An image can be sharp geometrically and still be limited by diffraction.

Common misconception

Angles are measured from the normal, not the surface. A virtual image is located by backward ray extensions; no rays physically converge there.

A further investigation

Find a pair of indices with a critical angle near 30°.

Check your understanding

Total internal reflection requires…

• Higher to lower index
• Lower to higher index
• Equal indices

Model limits

Homogeneous, lossless media; no dispersion or Fresnel intensity calculation.

OpenStax · Refraction