Total internal reflection happens when all the light in a dense medium is reflected at the boundary instead of refracting out. You test a given ray with a direction check, then an angle check.
This lesson is part of SPM Physics light and optics. It relies on applying refraction and refractive index.
What are the two checks?
Apply them in this order. Stop at the first check that fails.
- Direction: is the light going from a denser medium to a less dense medium, such as glass to air?
- Angle: is the angle of incidence greater than the critical angle c, where sin c = 1 ÷ n?
Worked example: critical angles
For glass with n = 1.50: sin c = 1 ÷ 1.50 = 0.667, so c = 41.8°.
For water with n = 1.33: sin c = 1 ÷ 1.33 = 0.752, so c = 48.8°.
Glass has the higher refractive index, so its critical angle is smaller and light is totally reflected more easily.
Testing two rays
A ray inside a glass block (n = 1.50) reaches the glass–air boundary.
Ray 1, angle of incidence 50°. The ray goes from glass to air, so direction passes. 50° is greater than 41.8°, so it is totally reflected.
Ray 2, angle of incidence 30°. Direction passes, but 30° is less than 41.8°, so most of the light refracts out. Going from glass to air, sin r = 1.50 × sin 30° = 0.75, so r = 48.6°. A small part is also reflected.
Where is it used?
An optical fibre has a glass core surrounded by a material of lower refractive index. Light enters the core and hits the boundary at angles above the critical angle, so it reflects along the fibre. A right-angled glass prism with n = 1.50 turns light through 90° or 180°, because the ray meets the long face at 45°, which is above 41.8°.
The mistake that costs marks
The common slip is to apply total internal reflection to light going from air into glass. It cannot happen in that direction, because air is less dense than glass.
| Situation | Wrong | Right |
|---|---|---|
| Air to glass at 80° | Totally reflected | Refracts into the glass, since the direction check fails |
| Glass to air at 30° | Totally reflected | Refracts out, since 30° is below 41.8° |
Write both checks in your answer, and use the word “greater” for the angle comparison.
Check yourself
The refractive index of a plastic is 1.60. Calculate its critical angle, and state whether a ray inside the plastic with an angle of incidence of 35° at the plastic–air boundary is totally reflected.
Answer
sin c = 1 ÷ 1.60 = 0.625, so c = 38.7°.
The ray travels from plastic to air, so direction passes. But 35° is less than 38.7°, so the ray is not totally reflected. It refracts out, with most of the light passing into the air.
What to study next
Move on to explaining optical-instrument principles, or test the chapter with the light and optics practice set.
The units and significant-figure checker helps with angle answers. If you want a teacher to go through your reasoning on new cases, see online one-to-one Physics tuition.