Practice questions · Critical angle and TIR

Two conditions. No leak.

Seven original Cambridge-style questions. They drill the two conditions for total internal reflection, the exact definition of the critical angle, and the absolute fact that no refracted ray survives past it.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

Hold these three lines in your head

Denser to less dense. Past the critical angle. Nothing escapes.

Two conditions. Light must travel from the denser to the less dense medium, and the angle of incidence must be greater than the critical angle.
Critical angle. The angle of incidence in the denser medium for which the angle of refraction is 90°.
No leak. Past the critical angle there is no refracted ray. All of the light reflects.

[2 marks]

State the two conditions necessary for total internal reflection to occur.

The light must be travelling from a more dense to a less dense medium (toward the boundary from inside the denser one). ✓
The angle of incidence must be greater than the critical angle. ✓

Both conditions are needed. Stating only the angle condition usually loses a mark.

[2 marks]

Define the critical angle.

The critical angle is the angle of incidence, in the denser medium, for which the angle of refraction is 90°. ✓✓

"In the denser medium" and "refraction is 90°" are both needed for full marks.

[3 marks]

A ray of light inside a glass block travels toward the surface. Describe what happens to the light when the angle of incidence is:

(a) less than the critical angle, [1] (b) exactly equal to the critical angle, [1] (c) greater than the critical angle. [1]

(a) Most of the light refracts and escapes into the air, with a weak reflected ray inside. ✓

(b) The refracted ray travels along the surface (angle of refraction = 90°). ✓

Analysis

[2 marks]

A student describes total internal reflection like this: "When the angle is bigger than the critical angle, most of the light reflects back but a faint refracted ray still escapes." Explain what is wrong with this statement.

There is no refracted ray at all once the angle of incidence exceeds the critical angle. ✓
The reflection is total: 100 percent of the light is reflected back, so no faint ray escapes. ✓

The word "total" is literal. Drawing or describing a leaky refracted ray is a frequently penalised error.

Diagram

[3 marks]

The diagram shows a ray of light entering a right-angled glass prism and striking the sloping face from inside. The critical angle for the glass is 42°.

A ray meets the sloping face from inside the prism at 45° to the normal.

(a) Explain why the ray is totally internally reflected at the sloping face. [2] (b) State the angle of reflection at the sloping face. [1]

(a) The angle of incidence at the sloping face is 45°, which is greater than the critical angle of 42°, and the light is inside the denser glass. Both conditions for TIR are satisfied. ✓✓

(b) Angle of reflection = 45° (equal to the angle of incidence). ✓

45° prisms are used in periscopes and binoculars precisely because 45° beats the critical angle of ordinary glass.

Analysis

[2 marks]

High-quality periscopes and binoculars use right-angled glass prisms rather than ordinary silvered mirrors to turn the light. Suggest two advantages of using prisms that rely on total internal reflection.

Total internal reflection reflects 100 percent of the light, so the image is brighter than with a mirror, which absorbs some light. ✓
There is no silvered coating to scratch, tarnish, or peel, so the prism stays effective and gives no faint double images. ✓

A plane mirror loses a little light at the glass surface and at the coating. A TIR prism loses none.

Analysis

[3 marks]

Diamond has a very small critical angle of about 24°, while window glass has a critical angle of about 42°.

(a) Explain what a smaller critical angle means for how easily light is totally internally reflected. [2] (b) Use this to suggest why a cut diamond sparkles much more than a similarly shaped piece of glass. [1]

(a) A smaller critical angle means a larger range of incidence angles will exceed it, so light is totally internally reflected far more easily inside the diamond. ✓✓

(b) Light entering a diamond bounces around by TIR many times before leaving, so more light is sent back out toward the eye, giving the strong sparkle. ✓

Small critical angle, easy TIR, lots of internal bounces. That is the optics of a sparkle.

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.