Home › Learning Hub › IGCSE Physics › 3b Reflection and refraction
Topic 3 · 3.2.1–3.2.2

Reflection and refraction of light

Core and Extended · Papers 1–6

🎯What you need to be able to do

  • Define normal, angle of incidence and angle of reflection; state and use the law of reflection.
  • Describe the image in a plane mirror; use constructions and calculations for it EXTENDED.
  • Describe refraction through transparent blocks and an experiment to show it; explain critical angle and total internal reflection.
  • Define refractive index; use \( n = \dfrac{\sin i}{\sin r} \) and \( n = \dfrac{1}{\sin c} \); describe optical fibres EXTENDED.

📚The physics

Reflection

The normal is a line at 90° to the surface where the ray strikes it. Angles are always measured from the normal. The law of reflection: the angle of incidence equals the angle of reflection.

Left: a ray strikes a plane mirror and reflects, with equal angles of incidence and reflection measured from the dashed normal. Right: an object in front of a plane mirror; rays from its tip reflect from the mirror and, traced back as dashed lines, appear to come from an image the same distance behind the mirror, upright and the same size.
The image in a plane mirror is the same size, the same distance behind the mirror, upright and virtual.

A virtual image cannot be formed on a screen: the reflected rays only appear to come from it. EXTENDED To locate an image by construction, draw two rays from a point on the object to the mirror, reflect each with equal angles, then extend the reflected rays back behind the mirror: they meet at the image.

Refraction

A ray of light enters a rectangular glass block at an angle of incidence i and bends towards the normal, with a smaller angle of refraction r. It leaves the opposite face bending away from the normal, emerging parallel to the incident ray but shifted sideways.
Refraction is caused by the change in speed at the boundary.

To show refraction, place a glass or Perspex block on paper, shine a ray box beam at it (or use optics pins), mark the rays, then join them through the block and measure the angles with a protractor. Blocks of different shapes (rectangular, semicircular, triangular prism) all show the same rules. A ray along the normal passes straight through.

The critical angle is the angle of incidence (inside the denser material) for which the angle of refraction is 90°. At larger angles all the light is reflected: total internal reflection. Examples: prisms in periscopes and binoculars, the sparkle of diamonds, optical fibres.

Three semicircular glass blocks, each with a ray aimed at the centre of the flat face from inside. At 30 degrees, less than the critical angle, the ray refracts out into the air, with a weak reflection. At 42 degrees, the critical angle, the refracted ray runs along the surface. At 55 degrees, greater than the critical angle, all the light is reflected back into the glass.
Total internal reflection needs light going from a denser to a less dense material, at more than the critical angle.

Refractive index EXTENDED

The refractive index n is the ratio of the speeds of a wave in two regions: \( n = \dfrac{\text{speed of light in air (vacuum)}}{\text{speed of light in the material}} \).

\[ n = \frac{\sin i}{\sin r} \qquad n = \frac{1}{\sin c} \]
A ray of light zigzags along the core of an optical fibre, totally internally reflecting each time it meets the boundary.
EXTENDED Optical fibres carry visible light or infrared signals for telephones, cable television and broadband.

✏️Worked example

EXTENDED A ray enters a Perspex block with an angle of incidence of 40°; the angle of refraction is 26°. (a) Calculate the refractive index of the Perspex. [2] (b) Calculate its critical angle. [2] (c) Calculate the speed of light in the Perspex (speed in air 3.0 × 108 m/s). [2]

(a) \( n = \dfrac{\sin 40^\circ}{\sin 26^\circ} = \dfrac{0.643}{0.438} = \) 1.47.

(b) \( \sin c = \dfrac{1}{1.47} = 0.681 \), so c = 43°.

(c) \( v = \dfrac{3.0 \times 10^8}{1.47} = \) 2.0 × 108 m/s.

Check it. n must be greater than 1, the angle in the block must be smaller than in air, and the speed must be less than in air: all three agree.
Dividing the angles. n = sin i / sin r, not i / r: 40 / 26 = 1.54, which is wrong.

📝Practise

In the style of the multiple-choice, theory and practical papers. EXTENDED marks Supplement content.

1. (Theory.) A ray strikes a plane mirror. State the name of the line drawn at 90° to the mirror where the ray strikes, state the law of reflection, and give three characteristics of the image of a toy placed in front of the mirror. [5] (Modelled on 0625/32 June 2026 Q7(a).)
The normal. Angle of incidence = angle of reflection. The image is the same size as the toy, the same distance behind the mirror as the toy is in front, upright, virtual (and laterally inverted).
2. (Multiple choice.) A ray strikes a plane mirror. Which angle is always equal to the angle of reflection? A: the angle between the incident ray and the mirror. B: the angle between the incident ray and the normal. C: the angle between the reflected ray and the mirror. D: the angle between the incident and reflected rays.
B — the angle of incidence.
3. (Multiple choice.) EXTENDED Green light of wavelength 540 nm in air slows from 3.0 × 108 m/s to 2.0 × 108 m/s in glass. What is its wavelength in the glass? A: 360 nm. B: 540 nm. C: 810 nm. D: 1100 nm. (Modelled on 0625/22 June 2026 Q18.)
A. The frequency does not change, so λ is proportional to v: 540 × 2.0 / 3.0 = 360 nm.
4. (Theory.) EXTENDED The refractive index of diamond is 2.42. Calculate its critical angle. [2]
sin c = 1 / 2.42 = 0.413; c = 24°. Such a small critical angle means light is often totally internally reflected, so diamonds sparkle.
5. (Theory.) EXTENDED Light enters water (n = 1.33) with an angle of incidence of 60°. Calculate the angle of refraction. [2]
sin r = sin 60° / 1.33 = 0.866 / 1.33 = 0.651; r = 41°.
6. (Practical.) Describe how to trace the path of a ray through a rectangular glass block using optics pins. [4]
Draw round the block on paper on a pin board. Put two pins in line on one side (the incident ray). Looking through the block from the other side, place two more pins in line with the images of the first two. Remove the block; join the pins and join the entry and exit points to show the ray inside the block; draw normals and measure angles with a protractor.
7. (Theory.) State two conditions for total internal reflection. [2]
The light travels from a denser to a less dense material (e.g. glass to air); the angle of incidence is greater than the critical angle.
8. (Theory.) EXTENDED Explain why optical fibres are used to carry broadband data. [2]
Glass is transparent to visible light and some infrared, so the signal travels far with little loss, kept inside the fibre by total internal reflection; visible light and short-wavelength infrared can carry data at high rates.

🔗Go deeper — other people’s work

These are external resources, not mine. If one stops working, tell me and everything above it on this page still stands.

  • PhET “Bending Light” — refraction, refractive index and total internal reflection
  • The Physics Classroom — reflection and plane mirrors