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Cambridge IGCSE Physics · 0625

Chapter 3: Waves — Part 3

Topic 3.2.2 · Refraction of light

Refraction at a boundary

The normal, angle of incidence and angle of refraction are used at the boundary between two media.

When light goes into a denser medium (air to glass) it slows down and bends towards the normal. When it leaves into a less dense medium it speeds up and bends away from the normal.

Show this with rays through rectangular and triangular transparent blocks.

Light through a rectangular glass block: ray towards the normal on entering glass, away from the normal on leaving, with i and r labelled from the normal.
Diagram 1: Light through a rectangular glass block: ray towards the normal on entering glass, away from the normal on leaving, with i and r labelled from the normal.

Refractive index and TIR

Refractive index n is the ratio of the speeds of a wave in two regions. For air to glass, n = sin i / sin r (i in air, r in glass).

The critical angle c is the angle of incidence in the denser medium for which the refracted ray runs along the boundary (r = 90°). n = 1 / sin c.

If i > c, total internal reflection (TIR) occurs. Optical fibres use TIR to carry signals (telecommunications).

A ray of light in air hits a glass block with angle of incidence 40° and angle of refraction 25°. Calculate the refractive index of the glass.

Worked example: refractive index is sin 40 over sin 25 equals 1.52
n = sin i / sin r = 1.52. i is the angle in air.

Glass has refractive index 1.50. Calculate the critical angle for light travelling in this glass towards air.

Worked example: critical angle is inverse sine of 1 over 1.50 equals 42 degrees
sin c = 1/n, so c = 42° (2 s.f.).

Describe TIR with a semicircular block and with everyday examples (fibre, reflecting prism).

Total internal reflection: ray in glass towards air, i greater than critical angle c, reflected inside; optical fibre showing TIR along the core.
Diagram 2: Total internal reflection: ray in glass towards air, i greater than critical angle c, reflected inside; optical fibre showing TIR along the core.

Exam Traps

  • TIR only happens when light is in the denser medium heading towards the less dense medium, with i greater than c — not from air into glass.

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