Wave Interaction: Reflection, Refraction and Lenses
Reflection at Plane Surfaces
When a wave strikes a smooth, flat surface, it is reflected. The key rule is that the angle of incidence equals the angle of reflection — both angles are measured from the normal, which is an imaginary line at right angles to the surface at the point of contact.
The incident ray, the reflected ray and the normal all lie in the same plane. During reflection, the wave speed, frequency and wavelength all remain unchanged — only the direction of travel changes. A plane (flat) mirror forms a virtual image: the image appears to be behind the mirror, is the same size as the object, is the same distance behind the mirror as the object is in front, and is laterally inverted (left and right swapped).
Law of reflection: angle of incidence = angle of reflection (both from the normal). During reflection, wave speed, frequency and wavelength are unchanged. A plane mirror produces a virtual image the same size as and the same distance from the mirror as the object.
Refraction at Boundaries
Refraction occurs when a wave crosses the boundary between two media with different optical densities. The wave changes speed, and if it hits the boundary at an angle (not along the normal), it also changes direction.
The rules of refraction are:
• When a wave passes from a less dense medium into a denser medium (e.g. air into glass), it slows down and bends towards the normal.
• When a wave passes from a denser medium into a less dense medium (e.g. glass into air), it speeds up and bends away from the normal.
• The frequency stays the same at both sides of the boundary. The wavelength changes because \(\lambda = \frac{v}{f}\) and the speed changes.
Different wavelengths of light refract by different amounts when entering glass. Violet light slows more than red light, causing the colours to spread. This is how a prism separates white light into its spectrum.
To draw a refraction ray diagram correctly:
1. Draw the boundary between the two media (e.g. air and glass) as a solid line.
2. Draw the normal at the point of incidence — a dashed line at 90° to the boundary.
3. Draw the incident ray and label the angle of incidence (\(i\)) from the normal.
4. Draw the refracted ray on the other side of the boundary. If the ray enters glass from air, it bends towards the normal; the angle of refraction (\(r\)) is smaller than \(i\).
5. If the ray exits glass into air, it bends away from the normal; \(r > i\).
6. Label both media and indicate the direction of travel with arrows.
Lenses — Converging and Diverging
Lenses work by refracting light at two curved surfaces. There are two types:
A converging lens (convex lens) is thicker in the middle. Parallel rays of light passing through it bend and converge at the focal point on the far side. The distance from the lens centre to the focal point is the focal length.
A diverging lens (concave lens) is thinner in the middle. Parallel rays passing through it spread apart (diverge) and appear to come from a focal point on the same side as the incoming light.
Converging (convex) lens: thicker in the middle; parallel rays meet at the focal point. Diverging (concave) lens: thinner in the middle; parallel rays spread apart, appearing to come from a focal point on the same side as the light source.
To draw a converging-lens ray diagram, use three principal rays from the top of the object:
1. A ray parallel to the principal axis → refracts through the far focal point.
2. A ray through the optical centre of the lens → passes straight through without bending.
3. A ray through the near focal point → refracts to travel parallel to the principal axis.
The image depends on the object’s distance from the lens (measured in multiples of the focal length \(f\)):
Object beyond 2f: the image is real, inverted and diminished (smaller than the object). This is how a camera forms an image on its sensor.
Object at 2f: the image is real, inverted and the same size as the object, formed at 2f on the other side.
Object between f and 2f: the image is real, inverted and magnified (larger than the object). This is how a projector works.
Object closer than f: the refracted rays diverge and do not meet on the far side. When extended back, they appear to come from a point on the same side as the object — a virtual, upright and magnified image. This is how a magnifying glass works.
A real image is formed where light rays actually meet. It can be projected onto a screen. Images formed by converging lenses when the object is beyond the focal point are real.
A virtual image is formed where rays appear to come from when extended backwards — no light actually passes through the image position. It cannot be projected onto a screen. The image in a plane mirror and the magnifying glass image are both virtual. Virtual images are always upright; real images are always inverted (for a single converging lens).
Colour comes from the way a material absorbs, transmits and reflects different wavelengths. A red jumper looks red because it reflects red light and absorbs the other colours. A red filter transmits red light and absorbs the rest — it does not add colour to the light. A white surface reflects all visible wavelengths; a black surface absorbs almost all of them. A smooth surface such as a mirror gives specular reflection, where the rays all leave in the same direction. A rough surface scatters the rays in many directions, which is why it looks matt instead of shiny.