Critical Angle and Total Internal Reflection
Simple Explanation
When light travels from a denser medium toward a less dense one, at a specific angle (the critical angle), the refracted ray travels exactly along the boundary (90° from the normal). At angles greater than this critical angle, no light refracts out at all — instead, ALL of it reflects back into the denser medium, a phenomenon called total internal reflection.
Why Do We Need It?
Total internal reflection is the working principle behind optical fibres, which carry internet and telephone signals as light pulses across huge distances with minimal loss.
Formula
Critical Angle
sinθc = 1/n
The critical angle is the angle of incidence (in the denser medium) at which the refracted ray travels exactly along the boundary (refraction angle = 90°) — beyond this angle, total internal reflection occurs.
- θc
- — Critical angle, measured from the normal
- n
- — Refractive index of the denser medium (light travels from denser to less dense medium)
When to use it: Use to find the critical angle for light travelling from a denser medium (like glass or water) toward a less dense one (like air), given the denser medium's refractive index.
Worked Example
Finding the critical angle for glass
Glass has a refractive index of 1.5. Find the critical angle for light travelling from glass into air.
Why Does This Work?
As the angle of incidence increases (from a denser to a less dense medium), the angle of refraction increases even faster (following Snell's law) — at the critical angle, the refraction angle reaches exactly 90°; beyond this, Snell's law would require sinθ₂ to exceed 1, which is impossible, so instead all the light reflects internally rather than refracting out.
Real-Life Example
Optical fibres carrying internet data
Optical fibre cables carry light signals across vast distances (undersea cables span entire oceans) with minimal signal loss.
Light inside the fibre core repeatedly strikes the core-cladding boundary at an angle greater than the critical angle, undergoing total internal reflection over and over — this keeps the light signal trapped inside the fibre core, travelling huge distances with very little loss.
Practice
A medium has a refractive index of 1.33 (water). Find its critical angle for light travelling from water into air.
HardCommon mistake
Applying the critical angle formula when light travels from a LESS dense medium into a denser one — total internal reflection and the critical angle only apply when light travels from denser to less dense; light entering a denser medium always refracts (never totally internally reflects).
Quick Review
- sinθc = 1/n gives the critical angle for light in a denser medium (n) approaching a less dense one.
- Beyond the critical angle, total internal reflection occurs — no light refracts out.
- Optical fibres use repeated total internal reflection to carry light signals over long distances.