← Refraction

Total internal reflection

Petrine shines a laser inside a glass block toward its top surface, first steeply, then at a larger and larger angle from the normal. At a small angle, most of the light leaves the glass. Past one particular angle, none of it leaves: the whole beam reflects back down into the glass.

Light trying to LEAVE a dense medium can be trapped. This lesson describes that trapping, and names the angle where it begins.

Set the scene: the light travels in the optically denser medium, the glass, and strikes the boundary with the less dense air.

Leaving a denser medium, the refracted ray bends AWAY from the normal: the angle outside is larger than the angle inside.

At a small angle of incidence, most of the light refracts out into the air, bent away from the normal. A little reflects back inside.

As the angle of incidence grows, the refracted ray leans further and further toward the surface.

At one particular angle of incidence, the refracted ray lies along the surface itself. That threshold angle is called the critical angle.
airglass30°30°49°below the critical angle
Below the critical angle: most of the light refracts out, bent away from the normal.
airglass42°42°at the critical angle, about 42° for this glass and air
At the critical angle: the refracted ray skims along the surface.
Past the critical angle, no refracted ray is possible: ALL of the light reflects back into the glass, and none escapes. This complete trapping is called total internal reflection.
airglass55°55°past the critical angle
Past the critical angle: no light escapes. The whole beam reflects back inside.

The reflected beam obeys the reflection law you already use: it leaves at the same angle from the normal as it arrived, on the other side.

For Petrine's glass and air, the critical angle is about 42°. Strike the surface at 50° from the normal, and the beam has no way out.

Light inside a diamond strikes the boundary with air at 40° from the normal. The critical angle for diamond and air is about 24°. What happens to the light?

The light is in the denser medium, heading for a less dense one: the trapping setup.

Compare the angle of incidence with the critical angle: 40° is past 24°.

Past the critical angle, all of the light reflects back inside and none refracts out.

The whole beam reflects back into the diamond: total internal reflection.

Light inside the same diamond strikes the boundary at 15° from the normal. What happens now?

Compare again: 15° is below the 24° critical angle.

Below the critical angle, the light can still get out.

Most of it refracts out into the air, bent away from the normal; a little reflects back inside.

Most of the light refracts out of the diamond; only a little reflects back.

Light inside a diamond strikes the boundary with air at an angle past the critical angle. What happens to the light?

Light inside a glass paperweight strikes the boundary with air at an angle smaller than the critical angle. What happens to the light?

Maud says: 'Past the critical angle, none of the light leaves the glass: the boundary reflects all of it back inside.' Is Maud correct?

Your turn

Which statement describes total internal reflection?

A swimmer underwater at night shines a flashlight up toward the surface at 60° from the normal. The critical angle for water and air is about 49°. What happens to the beam at the surface?

Light inside a glass block strikes the top surface at 55° from the normal, past the glass-air critical angle, and totally internally reflects. At what angle from the normal does the reflected beam travel back into the glass?