Reflection: light bouncing off surfaces
When light hits a smooth, shiny surface such as a mirror, it bounces off in a predictable way. To describe this we always measure angles from the normal, an imaginary line drawn at right angles to the surface at the point where the ray lands, not from the surface itself.
- Law of reflection
- The angle of incidence equals the angle of reflection, \( \theta_i = \theta_r \), and the incident ray, the reflected ray and the normal all lie in the same plane.
A smooth mirror gives a clear image because all the parallel rays reflect together; this is specular reflection. A rough surface such as paper scatters rays in all directions, which is called diffuse reflection, and it is why you can read a page from any angle but cannot see your face in it.
Where this is assessed
Ray optics is prime Criterion B and Criterion C territory: you plan a ray-box experiment, then process angle measurements into a pattern. Always measure from the normal, or your whole data set will be wrong.
Refraction and Snell's law
When light passes from one material into another, for example from air into glass, it changes speed. If it meets the boundary at an angle, that change of speed makes it change direction too. This bending is called refraction.
Going into a denser material such as glass, light slows down and bends towards the normal. Coming back out into air it speeds up and bends away from the normal. How much a material slows light is captured by its refractive index, \( n \).
Here \( i \) is the angle of incidence and \( r \) is the angle of refraction, both measured from the normal. A larger \( n \) means the light bends more. This relationship is known as Snell's law.
A ray of light travels from air into glass. The angle of incidence is 40° and the angle of refraction is 25°. Find the refractive index of the glass.
Refractive index has no units
It is a ratio of two sines, so the units cancel. For everyday materials \( n \) is always greater than 1: air is about 1.0, water about 1.33 and glass about 1.5.
Total internal reflection and the critical angle
When light travels from a dense material such as glass towards a less dense one such as air, it bends away from the normal. If you keep increasing the angle of incidence, the refracted ray bends closer and closer to the boundary until, at one special angle, it runs right along it. That angle is the critical angle, \( c \).
Push past the critical angle and the light can no longer escape at all. Instead it reflects entirely back inside the material, obeying the law of reflection. This is total internal reflection (TIR).
| Angle of incidence | What happens |
|---|---|
| Less than \( c \) | Most light refracts out, a little reflects |
| Equal to \( c \) | Refracted ray travels along the boundary |
| Greater than \( c \) | Total internal reflection, all light stays inside |
TIR is how optical fibres work: light bounces down the inside of a thin glass thread, staying trapped even as the cable curves, which lets it carry telephone and internet signals over long distances with very little loss. The same effect makes diamonds sparkle and lets a periscope's prisms redirect light cleanly.
The electromagnetic spectrum
Visible light is only a thin slice of a much larger family of waves that all travel at the same speed in a vacuum, the speed of light. Together they form the electromagnetic spectrum, ordered here from longest wavelength (lowest frequency) to shortest wavelength (highest frequency).
| Wave | A typical use |
|---|---|
| Radio waves | Broadcasting television and radio |
| Microwaves | Cooking food and mobile phone signals |
| Infrared | Remote controls and thermal imaging |
| Visible light | Seeing and optical fibre communication |
| Ultraviolet | Security marking and sterilising water |
| X-rays | Imaging bones in medicine |
| Gamma rays | Sterilising equipment and treating cancer |
Learn the order both ways
A common memory aid is "Raging Martians Invaded Venus Using X-ray Guns": Radio, Microwave, Infrared, Visible, Ultraviolet, X-ray, Gamma. As you move up the list, frequency and energy rise while wavelength falls, so the high-energy end (UV, X-rays, gamma) is the one that can damage cells.
Check yourself
Cover the answers and try each first.
1. A ray hits a mirror at an angle of 35° to the normal. What is the angle of reflection, and why? +
By the law of reflection, the angle of reflection equals the angle of incidence, so it is 35°, also measured from the normal.
2. Light enters water (\( n = 1.33 \)) from air at an angle of incidence of 30°. Find the angle of refraction. +
Rearrange \( n = \dfrac{\sin i}{\sin r} \) to \( \sin r = \dfrac{\sin i}{n} = \dfrac{\sin 30°}{1.33} = \dfrac{0.5}{1.33} = 0.376 \). So \( r = \sin^{-1}(0.376) = \) 22° (to the nearest degree). The ray bends towards the normal, as expected on entering a denser material.
3. Name one use of infrared radiation and one use of gamma rays. +
Infrared is used in remote controls and thermal imaging cameras. Gamma rays are used to sterilise medical equipment and to treat cancer (radiotherapy).
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