Total internal reflection explains how light can be trapped inside a material instead of passing through a boundary. To understand it, you must track the refractive indices, the incident angle, and the critical angle.

When Total Internal Reflection Occurs

Total internal reflection happens at a boundary between two transparent media. The light must start in the medium with the greater index of refraction and travel toward a medium with the smaller index. As the angle of incidence increases, the refracted ray bends farther away from the normal. This trend continues until the refracted ray reaches the boundary itself. If the angle is increased even more, the light no longer passes into the second medium.

Two conditions must both be satisfied.

• The light must go from higher refractive index to lower refractive index.

• The angle of incidence must be large enough.

If either condition fails, total internal reflection does not occur. For example, light going from air into glass can refract and reflect, but it cannot undergo total internal reflection at that boundary because it is entering the higher-index medium.

The Critical Angle

The special angle that separates ordinary refraction from total internal reflection is called the critical angle. It is measured in the higher-index medium, from the normal to the surface. At this angle, the refracted ray is not directed into the second medium. Instead, it travels along the boundary, making a $90^\circ$ angle with the normal.

Schematic of total internal reflection geometry at a boundary with $n_1>n_2$. The diagram emphasizes that the critical angle $\theta_c$ is measured in the higher-index medium from the normal, and that the refracted ray is tangent to the interface at $\theta_c$. This is the limiting case used to derive $\sin\theta_c=\dfrac{n_2}{n_1}$. Source

For a boundary where $n_1>n_2$, the critical angle can be found from the refractive indices.

This equation only applies when the incident medium has the larger refractive index. If $n_1 \le n_2$, total internal reflection cannot occur for that direction of travel, so a useful critical angle is not defined. A smaller critical angle means total internal reflection begins at a smaller angle of incidence.

Below, At, and Above the Critical Angle

At the same boundary, three different behaviors are possible depending on the incident angle:

Ray diagrams for the same boundary as the incident angle increases. The middle case highlights the defining feature of the critical angle: the refracted ray travels along the interface (i.e., the refracted angle is $90^\circ$ to the normal). Above this angle, the diagram shows only a reflected ray in the original (higher-index) medium. Source

• Below the critical angle: Some light refracts into the second medium, and some may reflect. The transmitted ray bends away from the normal because it is entering a lower-index medium.

• At the critical angle: The refracted ray travels exactly along the surface. This is the limiting case between refraction and total internal reflection.

• Above the critical angle: No refracted ray enters the second medium. All the light is reflected back into the original medium, so the interaction is total internal reflection.

These three cases are especially important in ray diagrams. The critical angle marks the boundary between a situation with a transmitted ray and a situation with only a reflected ray.

Interpreting What "All Light Reflects" Means

Within the geometric optics model, all light reflects means no refracted ray is drawn beyond the boundary once the incident angle exceeds the critical angle. The boundary still matters because the light changes direction there, but the light stays entirely in the original medium. This is why total internal reflection can trap light inside transparent materials. The effect is not caused by a mirror coating. It comes from the change in refractive index at the boundary itself. For AP Physics 2 reasoning, once total internal reflection begins, the second medium no longer carries a transmitted ray in the ray diagram.

Interpreting Ray Diagrams and Problems

In problems, first identify which medium the light starts in. Then compare the two indices of refraction. If the light is moving toward a lower-index medium, total internal reflection is possible. Next compare the incident angle with the critical angle:

• If $\theta_i<\theta_c$, refraction occurs.

• If $\theta_i=\theta_c$, the refracted ray runs along the surface.

• If $\theta_i>\theta_c$, total internal reflection occurs.

A common mistake is to think that a large angle alone guarantees total internal reflection. It does not. The direction of travel matters just as much as the size of the angle. Another common mistake is measuring the angle from the surface instead of from the normal. In this topic, all relevant angles are measured from the normal.