Reflection and Refraction of Waves

What happens at a boundary?

A wave reaching the boundary between two materials can be reflected back into the first material or pass into the second. This boundary is called an interface. Light arriving at a glass surface, for example, can partly reflect and partly pass into the glass.

A ray diagram represents the direction in which light travels using straight lines with arrows. To describe what happens at a surface, draw a normal: a line at right angles to the surface, through the point where the ray meets it. All the angles used here are measured between a ray and this normal.

Reflection: returning into the same material

In reflection, a wave returns into the material it came from. Light reflects from mirrors, and reflected sound can produce an echo.

The incoming ray is the incident ray. The outgoing ray is the reflected ray. For a plane mirror, the law of reflection is:

$$\text{angle of incidence} = \text{angle of reflection}$$

For example, a ray arriving at $30^\circ$ to the normal leaves at $30^\circ$ to the normal on the other side. Its direction changes, but its speed, frequency and wavelength do not change because it remains in the same material.

Investigating reflection from a plane mirror

You need a ray box with a thin single slit, a plane mirror and holder, white paper, a pencil, a ruler and a protractor.

1. Place the paper flat on the desk and stand the mirror upright on it. Mark the position of its reflecting surface.
2. Choose a point on that line and draw a normal at right angles to it.
3. Dim the room lighting so that the ray is easy to see. Direct a narrow ray towards the chosen point on the mirror.
4. Mark at least two points along each of the incident and reflected rays. Move the apparatus aside and join the points with a ruler.
5. Use a protractor to measure the angle of incidence and the angle of reflection from the normal.
6. Repeat for several different angles of incidence, keeping the mirror aligned with its marked position. Record the pairs of angles in a table.

The investigation is complete when you have several clear ray paths and angle pairs to compare. The angles of incidence and reflection should be equal, allowing for measurement uncertainty. A narrow ray makes its direction easier to mark precisely.

Do not look directly into the ray box. Some ray boxes become hot, so let them cool before handling them. Keep the mirror secure and handle its glass edges carefully. Dim the lighting only enough to see the rays while still working safely.

Refraction: a change in speed

Waves travel at different speeds in different substances. Refraction happens when a wave passes into a material where its speed is different. If it enters at an angle to the normal, its direction changes too.

Light travels more slowly in glass than in air. When it enters glass at an angle, it bends towards the normal: the angle of refraction is smaller than the angle of incidence. When it leaves glass for air, it speeds up and bends away from the normal.

This is about the speed of the wave in each material, not simply how heavy or dense the material is. The useful rule is:

• Slower in the new material → towards the normal.
• Faster in the new material → away from the normal.

If the ray enters along the normal, its speed still changes, but its direction does not.

Why changing speed turns a wave

Imagine a straight wavefront approaching glass at an angle. A wavefront joins points at the same stage of their vibration, such as neighbouring crests. One end reaches the glass first and slows down while the other end is still travelling faster in air. This turns the wavefront, changing the direction of travel.

The wave's frequency stays the same as it crosses the boundary. Using the wave equation,

$$v = f\lambda$$

a decrease in speed with unchanged frequency means a decrease in wavelength. Light therefore has a shorter wavelength in glass than in air. On returning to air, its speed and wavelength increase again.

Measuring refraction through a prism

A rectangular glass prism, often called a glass block, lets you trace the ray at both the entry and exit surfaces. You need the prism, a ray box with a thin slit, white paper, a pencil, a ruler and a protractor.

1. Place the prism on the paper and trace its outline. Keep it in this position; the outline lets you realign it if it moves.
2. Choose an entry point on one face and draw a normal perpendicular to that face.
3. In dimmed lighting, direct a narrow ray into the prism at an angle to the normal.
4. Mark points along the incident and emergent rays. Mark where the light enters and leaves the prism.
5. Remove the prism. Use a ruler to draw the incident and emergent rays, then join the entry and exit points to show the ray inside the glass.
6. Measure the angle of incidence in air and the angle of refraction inside the glass, both from the entry normal.
7. Repeat at several angles, for example at regular intervals between $0^\circ$ and . Record the results in a table.

You now have ray paths and measurements showing that the ray bends towards the normal on entering the glass. Draw a separate normal at the exit point to show that it bends away from the normal on leaving. With parallel entry and exit faces, the emergent ray is parallel to the incident ray, but displaced sideways.

Use the same ray-box precautions as for the mirror investigation, and handle the glass prism carefully.

Different wavelengths can travel at different speeds

Wave speed in a material can also depend on wavelength. In glass, blue light travels more slowly than red light and is refracted more strongly.

White light contains a mixture of colours. A triangular glass prism can separate these colours because they are refracted by different amounts. This is dispersion. The prism separates colours already present in the white light; it does not create new colours.

Reflection

• A reflected wave returns into the material it came from.
• Angle of incidence = angle of reflection.
• Speed, frequency and wavelength remain unchanged in the same material.

Refraction

• Refraction results from a change in wave speed between materials.
• Slower → towards the normal; faster → away from the normal.