From mirrors and lenses to rainbows and optical fibres: how light travels, bends and creates colour, explained with diagrams, animations and worked examples.
Every time you open your eyes, you are detecting light that has travelled from a lamp, a screen or the Sun, bounced off objects, and entered your eye. Light is the fastest thing in the universe, it carries the energy that powers almost all life on Earth, and it can be bent, reflected, split into colours and even trapped inside glass threads to carry the internet. This article explains how light behaves: how it travels, how mirrors and lenses form images, why a straw looks bent in water, how a rainbow forms, and why a red apple looks red.
Light is a form of energy that we can see. Objects that make their own light, such as the Sun, flames and lamps, are luminous. Most things we see, like trees and books, are non-luminous: we see them only because they reflect light into our eyes. The Moon is non-luminous; it shines by reflecting sunlight.
Light travels in straight lines, which we draw as rays with arrows. This explains shadows: an opaque object blocks the rays, and the region behind it receives no light. It also explains the pinhole camera, which forms an upside-down image because rays from the top of an object cross as they pass through the tiny hole. Eclipses are shadows too. In a solar eclipse the Moon's shadow falls on part of the Earth; in a lunar eclipse the Earth's shadow falls on the Moon.
In a vacuum, light travels at c = 299 792 458 m/s, exactly, by the modern definition of the metre. For calculations, 3.00 × 10⁸ m/s is accurate enough. Light travels more slowly in materials: about 2.25 × 10⁸ m/s in water and about 2.0 × 10⁸ m/s in glass.
The Sun is about 1.5 × 10¹¹ m from the Earth. How long does its light take to arrive?
t = distance ÷ speed = 1.5 × 10¹¹ ÷ 3.0 × 10⁸ = 500 s ≈ 8.3 minutes.
So we see the Sun as it was a little over 8 minutes ago. A light-year, the distance light travels in a year, is about 9.46 × 10¹² km. It is a unit of distance, not of time.
Visible light is one small part of a large family of electromagnetic (EM) waves. All EM waves are transverse waves that travel at the same speed, c, in a vacuum and need no medium. They differ in wavelength and frequency, and are linked by c = f × λ. Visible light has wavelengths from roughly 400 nm (violet) to 700 nm (red), where 1 nm = 10⁻⁹ m.
Red light has a wavelength of 700 nm in air. Find its frequency.
f = c ÷ λ = 3.0 × 10⁸ ÷ 7.0 × 10⁻⁷ ≈ 4.3 × 10¹⁴ Hz.
Other EM waves have important uses and risks: radio waves carry broadcasts, microwaves heat food and carry mobile signals, infrared is felt as heat and used in remote controls, ultraviolet causes sunburn and can damage skin and eyes, X-rays image bones, and gamma rays are used in sterilising equipment and cancer treatment. The high-frequency waves (UV, X-rays, gamma rays) can damage living cells, so exposure is limited.
When light hits a surface it can be reflected, absorbed or transmitted. For reflection from a smooth mirror, the law of reflection applies:
angle of incidence (i) = angle of reflection (r)
Both angles are measured from the normal, an imaginary line at 90° to the surface at the point where the ray hits. The incident ray, the normal and the reflected ray all lie in one plane.
A rough surface such as paper scatters light in many directions (diffuse reflection), which is why we can see the paper from any angle. Only a smooth surface gives regular (specular) reflection and a clear image.
In a plane (flat) mirror the image is virtual (formed where rays only seem to come from, so it cannot be shown on a screen), upright, the same size as the object, as far behind the mirror as the object is in front, and laterally inverted (left and right appear swapped). That is why "AMBULANCE" is written backwards on the front of ambulances: drivers see it correctly in their mirrors. A periscope uses two plane mirrors to let you see over obstacles.
Curved mirrors: a concave (curved inward) mirror brings parallel rays to a focus and is used in torch and car-headlight reflectors, satellite dishes, and telescopes. A convex (curved outward) mirror spreads rays out and gives a wider field of view, so it is used as a car's wing mirror and in shops for security.
Refraction is the change in direction of light as it passes from one transparent material into another, caused by a change in its speed. When light slows down on entering a denser material such as glass, it bends towards the normal; when it speeds up on leaving, it bends away from the normal. If it enters along the normal, it slows but does not bend.
Snell's law: n = sin i ÷ sin r (light entering the material from air)
Refractive index: n = c ÷ v (speed of light in a vacuum ÷ speed in the material)
This law is named after Willebrord Snellius (early 1600s); it was described earlier by the Persian scientist Ibn Sahl around 984 CE. Typical values: air ≈ 1.00, water ≈ 1.33, glass ≈ 1.5, diamond ≈ 2.42.
Light in air strikes glass (n = 1.5) at an angle of incidence of 45°. Find the angle of refraction.
Step 1. n = sin i ÷ sin r, so sin r = sin i ÷ n = sin 45° ÷ 1.5 = 0.7071 ÷ 1.5 = 0.4714.
Step 2. r = sin⁻¹(0.4714) = 28° (to the nearest degree).
(a) Find the speed of light in water (n = 1.33). (b) A swimming pool is 2.0 m deep. How deep does it look when viewed from directly above?
(a) v = c ÷ n = 3.00 × 10⁸ ÷ 1.33 ≈ 2.26 × 10⁸ m/s.
(b) For viewing from above, apparent depth = real depth ÷ n = 2.0 ÷ 1.33 ≈ 1.5 m.
This is why a pool looks shallower than it is and a straw in water seems bent at the surface. Always take care when judging the depth of water.
When light travels from a denser material to a less dense one (for example, glass to air), it bends away from the normal. As the angle of incidence increases, the refracted ray bends closer and closer to the surface. At a particular angle called the critical angle (c), the refracted ray travels along the surface. For any larger angle, all the light is reflected back inside: this is total internal reflection (TIR). It needs two conditions: light travelling from a denser to a less dense medium, and an angle of incidence greater than the critical angle.
sin c = 1 ÷ n (for a material with air outside)
Find the critical angle for glass (n = 1.5) and for diamond (n = 2.42).
Glass: sin c = 1 ÷ 1.5 = 0.667, so c ≈ 42°.
Diamond: sin c = 1 ÷ 2.42 = 0.413, so c ≈ 24°.
The very small critical angle of diamond means light is trapped and bounces around inside many times before leaving, which is one reason diamonds sparkle.
Optical fibres are thin strands of glass or plastic. A central core is surrounded by a cladding of lower refractive index, so light entering one end hits the core–cladding boundary at angles greater than the critical angle and is totally internally reflected again and again, travelling along the fibre even round bends. Fibres carry telephone, television and internet signals as pulses of light with little loss, and doctors use bundles of them in endoscopes to look inside the body. The physicist Charles Kao's work in the 1960s on low-loss glass fibres for communication helped make this possible, and he shared the 2009 Nobel Prize in Physics.
A lens is a piece of transparent material with curved surfaces that refracts light to form images.
To draw an image from a converging lens, use two rays from the top of the object: one parallel to the axis, which refracts through the far focus, and one through the centre of the lens, which goes straight on. Where they meet is the top of the image. The image type depends on where the object is.
| Object position | Image | Example use |
|---|---|---|
| Beyond 2F | Real, inverted, smaller | Camera |
| Between F and 2F | Real, inverted, larger | Projector |
| Inside F | Virtual, upright, larger | Magnifying glass |
1 ÷ f = 1 ÷ u + 1 ÷ v and magnification m = v ÷ u = image height ÷ object height
u = object distance, v = image distance, f = focal length.
An object is placed 30 cm from a converging lens of focal length 10 cm. Find the image distance and magnification.
Step 1. 1 ÷ v = 1 ÷ f − 1 ÷ u = 1/10 − 1/30 = 3/30 − 1/30 = 2/30 = 1/15.
Step 2. v = 15 cm (positive, so the image is real and on the opposite side).
Step 3. m = v ÷ u = 15 ÷ 30 = 0.50: the image is half the size of the object (and inverted).
The human eye works like a camera. Light is refracted by the cornea, which does most of the bending, and then by the adjustable lens, which fine-tunes the focus. The iris controls the size of the pupil and so the amount of light. A real, inverted image forms on the retina, which contains light-sensitive cells: rods (work in dim light, no colour) and cones (work in bright light, and give colour vision). The optic nerve sends signals to the brain, which turns the image the right way up.
In 1666 Isaac Newton showed that white sunlight passing through a glass prism spreads into a band of colours, and that a second prism can recombine them into white; he described this work in his book Opticks (1704). The splitting is called dispersion. It occurs because different colours (wavelengths) travel at slightly different speeds in glass, so they refract by different amounts. Violet bends the most and red the least. The order is red, orange, yellow, green, blue, indigo, violet (often remembered as ROYGBIV).
Rainbows form when sunlight enters raindrops, is refracted and dispersed, reflects off the back of the drop, and is refracted again as it leaves. You see a rainbow with the Sun behind you and rain in front. In a primary rainbow, red is on the outside and violet on the inside, and the bow appears about 42° from the point directly opposite the Sun.
Colour of objects. An opaque object has the colour of the light it reflects and absorbs the rest. A red apple reflects mostly red light and absorbs the others. A white object reflects all colours, a black object absorbs nearly all. Under green light, a red apple looks nearly black because there is no red light for it to reflect. A colour filter transmits only its own colour and absorbs the others.
| Light (additive mixing) | Paint and ink (subtractive mixing) | |
|---|---|---|
| Primary colours | Red, green, blue | Cyan, magenta, yellow |
| All three together | White | Dark (near black) |
| Example | Red + green light = yellow | Cyan + yellow paint = green |
Screens make every colour by mixing red, green and blue light; printers use cyan, magenta and yellow inks (plus black). The sky is blue because air molecules scatter short wavelengths (blue) more strongly than long ones, and sunsets are red because the light travels through more air, so much of the blue is scattered out of the beam.
Try each question before opening the answer.
The angle of reflection is 35° from the normal, so the angle from the surface is 90° − 35° = 55°.
2.0 m behind the mirror, so you appear 4.0 m from your image.
d = ct = 3.0 × 10⁸ × 1.3 ≈ 3.9 × 10⁸ m (about 390 000 km).
sin r = sin 40° ÷ 1.33 = 0.6428 ÷ 1.33 = 0.4833, so r ≈ 29°.
sin c = 1 ÷ 1.33 = 0.752, so c ≈ 49°.
1/v = 1/8 − 1/12 = 3/24 − 2/24 = 1/24, so v = 24 cm. m = 24 ÷ 12 = 2, so the image is real, inverted and twice as large.
The shirt reflects blue light and absorbs other colours. Red light contains no blue, so almost nothing is reflected.
The light must be travelling from a denser to a less dense medium, and the angle of incidence must be greater than the critical angle.
Low-cost experiments: use a ray box or a torch with a slit to trace rays at a plane mirror and measure i and r; trace the path of light through a rectangular glass block and a semicircular block to find refractive index and the critical angle; use a coin and a cup of water to show apparent depth; project a candle or window image with a magnifying glass to find its focal length; split sunlight with a prism or a CD (never look at the Sun directly); mix coloured light with filters. Laser pointers must be Class 1 or 2 and never aimed at eyes. Numerical values are rounded; please check that they match the data booklet used by your examination board.
This article is original EDUSAMBAM writing. Definitions, constants and historical facts were checked against the sources below. Diagrams are original and were not copied from any source.
Note on the numbers: refractive indices and wavelength ranges are rounded typical values. Please check them against your own syllabus or exam board specification before relying on them.
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