Refraction, Critical Angle & Total Internal Reflection
Refraction is the bending of light when it moves from one medium to another (speed changes). From a rarer → denser medium, a ray bends towards the normal; from a denser → rarer medium, it bends away from the normal.
Named Angles (at a boundary)
- Angle of incidence (i)
- Angle of refraction (r)
- Angle of emergence — equals the angle of incidence in a parallel-sided block
Refraction Through a Parallel-Sided Block
- Enter denser medium → ray slows and bends towards the normal.
- Exit to rarer medium → ray speeds up and bends away from the normal.
- Angle of emergence = angle of incidence (rays are parallel before entry and after exit).
Real vs Apparent Depth
Real depth is the object’s true depth. Apparent depth is the raised, seen position due to refraction at the surface.
Refractive Index (n)
Definitions
n = \(\sin i / \sin r\)(Snell’s law (ratio form))n = speed of light in air / speed of light in medium
Higher refractive index → greater bending at the surface.
Critical Angle (c) and Total Internal Reflection (TIR)
Key Ideas
- Critical angle (c) — angle of incidence for which the refracted ray emerges along the boundary.
- Total internal reflection — occurs when the ray is in the denser medium and i > c.
- At i = c, the refracted angle is 90° (along the boundary).
Useful Relation
\( \sin c = 1/n \) for a ray going from a medium of index n to air.
Optical Fibre — Application of TIR
- Conditions for TIR in fibre: light must be in the denser core; incidence angle > critical angle; no refraction out of the core.
- Medical endoscope: bundles of fibres carry illumination in and image out for internal viewing.
- Telecommunications: light/IR pulses confined by TIR carry huge data rates with low loss.
Common Mistakes
- Writing TIR when the ray is in the rarer medium — TIR only happens in the denser medium.
- Forgetting that at i = c, the refracted ray runs along the boundary (not back into the first medium).
- Confusing n = sin i / sin r with n = sin r / sin i — use the correct media assignment.
Summary Table
| Concept | Definition / Rule | Notes |
|---|---|---|
| Refraction | Rarer→Denser: bends towards normal; Denser→Rarer: away from normal | Speed decreases in denser media; increases in rarer media |
| Refractive index (n) | n = \(\sin i / \sin r\) , n = v_air / v_medium |
Higher n → more slowing/bending |
| Critical angle (c) | \(\sin c = 1/n\) (to air) |
At i = c the refracted ray skims the boundary |
| TIR | Occurs when ray in denser medium has i > c | Used in optical fibres (endoscopes, telecom) |
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