Refraction Ray Diagrams

Refraction Basics

Refraction is the change in direction of a wave when it passes from one medium to another due to a change in its speed.

When a wave crosses the boundary between two different materials, its speed changes. This change in speed causes the wave to bend.

If the wave moves from a less dense medium (where it travels faster) to a more dense medium (where it travels slower), it bends towards the normal line (an imaginary line perpendicular to the boundary).

Conversely, if the wave moves from a more dense medium to a less dense medium, it speeds up and bends away from the normal.

The amount of bending depends on the difference in density (or optical density) between the two media.

For example, light travelling from air into glass slows down and bends towards the normal because glass is optically denser than air. When it exits glass back into air, it speeds up and bends away from the normal.

Ray Diagrams for Refraction

A ray diagram shows the path of a wave as a straight line called a ray. When drawing refraction ray diagrams, the following terms are important:

• Incident ray: The incoming ray approaching the boundary.
• Normal: A dotted line perpendicular to the boundary at the point of incidence.
• Refracted ray: The ray that bends as it passes into the new medium.
• Angle of incidence ($i$): The angle between the incident ray and the normal.
• Angle of refraction ($r$): The angle between the refracted ray and the normal.

When drawing a refraction ray diagram:

1. Draw the boundary between the two media as a straight line.
2. Draw the normal as a dotted line perpendicular to the boundary at the point where the ray hits.
3. Draw the incident ray approaching the boundary at an angle $i$ to the normal.
4. Draw the refracted ray bending either towards or away from the normal depending on the media.

The bending can be predicted using the refractive indices of the two media. The refractive index ($n$) is a measure of how much a medium slows down light compared to air (which has $n \approx 1$).

The relationship between angles and refractive indices is given by Snell's Law:

$$n_1 \sin i = n_2 \sin r$$

where:

• $n_1$ = refractive index of the first medium
• $i$ = angle of incidence
• $n_2$ = refractive index of the second medium
• $r$ = angle of refraction

If $n_2 > n_1$, the ray bends towards the normal ($r < i$). If $n_2 < n_1$, the ray bends away from the normal ($r > i$).

For instance, if light passes from air ($n = 1.00$) into glass ($n = 1.50$) at an angle of incidence $30^\circ$, the angle of refraction can be calculated:

Using Snell's Law:

$$1.00 \times \sin 30^\circ = 1.50 \times \sin r$$

$$\sin r = \frac{\sin 30^\circ}{1.50} = \frac{0.5}{1.50} = 0.333$$

$$r = \sin^{-1}(0.333) \approx 19.5^\circ$$

So the refracted ray bends towards the normal at about $19.5^\circ$.

Applications of Refraction

Refraction explains many everyday phenomena and is essential in designing optical devices.

• Light passing from air to glass or water: Light slows down and bends towards the normal, which is why objects under water appear closer than they really are.
• Apparent depth: When looking into water, the bottom appears shallower because light bends away from the normal as it leaves water into air, making the object appear higher than its actual position.
• Use in lenses and optical instruments: Refraction is the principle behind lenses in glasses, cameras, and microscopes, which focus light by bending rays to form images. (See the "Convex & Concave Lenses" topic for detailed lens diagrams.)

For example, a straw in a glass of water looks bent at the surface because light rays refract as they pass from water to air.

For instance, if a fish is 1.2 m below the surface of water, the apparent depth $d_a$ is given by:

$$d_a = \frac{\text{real depth}}{n} = \frac{1.2}{1.33} \approx 0.9 \text{ m}$$

So the fish appears only 0.9 m below the surface.