O-Level Physics · Secondary 3 and 4
Light: Reflection, Refraction and Lenses
This topic studies how light behaves when it meets a mirror, crosses into a new material or passes through a lens. You learn the laws of reflection, how to calculate refractive index, when total internal reflection happens and how a thin converging lens forms images. These ideas explain periscopes, optical fibres, cameras, projectors and magnifying glasses. The topic builds on general wave properties, since refraction happens because light changes speed.
What the syllabus expects
- State and apply the laws of reflection and describe the image formed by a plane mirror
- Explain refraction in terms of a change in the speed of light
- Define refractive index and use n = sin i / sin r and n = c/v
- Explain total internal reflection, define the critical angle and use sin c = 1/n
- Describe applications of total internal reflection, such as optical fibres
- Describe the action of a thin converging lens using the terms principal axis, principal focus and focal length
- Draw ray diagrams to show the formation of real and virtual images by a converging lens
Reflection and plane mirrors
The laws of reflection state that the incident ray, the reflected ray and the normal all lie in the same plane, and that the angle of incidence equals the angle of reflection. Both angles are measured from the normal, the line drawn at 90° to the mirror at the point where the ray strikes it. The image in a plane mirror is the same size as the object, upright, laterally inverted (left and right swapped) and virtual, which means it cannot be formed on a screen because the rays only appear to come from it. The image is as far behind the mirror as the object is in front. If you stand 2.0 m from a mirror, your image is 2.0 m behind it and 4.0 m from you.
Refraction and refractive index
Refraction is the bending of light as it passes at an angle from one medium into another, caused by a change in speed. Light entering glass from air slows down and bends towards the normal. Light leaving glass into air speeds up and bends away from the normal. A ray travelling along the normal changes speed but does not bend. The refractive index n of a material is defined as the speed of light in a vacuum divided by the speed of light in the material, n = c/v, with c = 3.0 × 10⁸ m/s. For light entering the material from air, n = sin i / sin r, where i is the angle of incidence in air and r is the angle of refraction. Glass with n = 1.5 slows light to 3.0 × 10⁸ ÷ 1.5 = 2.0 × 10⁸ m/s. The frequency stays the same, so the wavelength becomes shorter.
Total internal reflection
When light travels from a denser medium, such as glass, towards a less dense one, such as air, it bends away from the normal. As the angle of incidence increases, the refracted ray gets closer to the boundary. At the critical angle c, the refracted ray just grazes along the boundary at 90°. If the angle of incidence is greater than the critical angle, no light is refracted out and all of it is reflected back inside. This is total internal reflection. Two conditions are needed: light must travel from a denser to a less dense medium, and the angle of incidence must be greater than the critical angle. The critical angle is given by sin c = 1/n, so for glass with n = 1.5, c is about 42°. Optical fibres use repeated total internal reflection to carry light signals for telecommunications and inside endoscopes.
Converging lenses and ray diagrams
A thin converging lens brings rays parallel to the principal axis together at the principal focus F. The focal length f is the distance from the optical centre of the lens to F. To draw a ray diagram, use two of three standard rays from the top of the object. A ray parallel to the principal axis refracts through F on the far side. A ray through the optical centre passes straight through. A ray through F on the near side emerges parallel to the axis. Where the rays meet is the top of the image. An object further than 2F from the lens gives a real, inverted, diminished image, as in a camera. An object at 2F gives a real, inverted image of the same size, also at 2F. An object between F and 2F gives a real, inverted, magnified image, as in a projector. An object closer than F gives a virtual, upright, magnified image, as in a magnifying glass.
Worked example
A ray of light in air strikes the surface of a glass block with an angle of incidence of 50°. The angle of refraction in the glass is 30°. The speed of light in air is 3.0 × 10⁸ m/s. Calculate (a) the refractive index of the glass, (b) the speed of light in the glass and (c) the critical angle of the glass.
- Refractive index: n = sin i / sin r = sin 50° ÷ sin 30° = 0.766 ÷ 0.500 = 1.532, which is 1.53 to 3 significant figures.
- Speed in glass: v = c/n = 3.0 × 10⁸ ÷ 1.532 = 1.96 × 10⁸ m/s.
- Critical angle: sin c = 1/n = 1 ÷ 1.532 = 0.653.
- c = sin⁻¹ 0.653 = 40.7°, keeping the unrounded value of n to avoid rounding errors.
Answer: (a) 1.53 (b) 1.96 × 10⁸ m/s (c) 40.7°
Common mistakes
- Measuring angles from the mirror or block surface instead of from the normal. Always draw the normal first and measure i and r from it.
- Writing n = sin r / sin i, which gives a value less than 1. The refractive index of glass or water is always greater than 1, so the angle in air goes on top.
- Thinking total internal reflection can happen when light goes from air into glass. It only happens when light travels from the denser medium towards the less dense one.
- Describing a plane mirror image as inverted. It is upright but laterally inverted.
- Drawing ray diagrams freehand, without arrows, or showing the lines behind a lens for a virtual image as solid. Use a ruler, add arrows and draw virtual rays as dashed lines.
- Confusing F with 2F when deciding which case applies. Mark both points on each side of the lens before drawing any rays.
Exam tips
- In refraction calculations, check that your refractive index is greater than 1 and that the ray bends towards the normal on entering the denser medium. Both are quick checks on your working.
- When explaining total internal reflection, state both conditions in full. Answers that give only one condition usually lose a mark.
- For ray diagrams, use a sharp pencil and ruler, draw at least two standard rays, and finish by stating three properties of the image: real or virtual, upright or inverted, magnified or diminished.
Practice questions
1. Easy: A ray of light strikes a plane mirror at an angle of 35° to the surface of the mirror. What is the angle of reflection, and what is the angle between the incident and reflected rays?
Show answer
The angle of incidence is measured from the normal: 90° − 35° = 55°. So the angle of reflection is 55°, and the angle between the two rays is 55° + 55° = 110°.
2. Medium: Light travels at 2.25 × 10⁸ m/s in a liquid. Taking c = 3.0 × 10⁸ m/s, find the refractive index of the liquid and its critical angle.
Show answer
n = c/v = 3.0 × 10⁸ ÷ 2.25 × 10⁸ = 1.33. sin c = 1/n = 2.25 ÷ 3.0 = 0.75, so c = sin⁻¹ 0.75 = 48.6°.
3. Harder: An object is placed 15 cm from a thin converging lens of focal length 10 cm. Describe the image formed and state a device that uses this arrangement.
Show answer
The object is between F (10 cm) and 2F (20 cm), so the image is real, inverted and magnified, formed beyond 2F on the other side of the lens. A careful scale ray diagram places it about 30 cm from the lens and about twice the height of the object. A projector uses this arrangement.
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