KAHIBARO
Table of Contents
Geometrical optics begins with a very useful idea, light can often be treated as traveling along straight lines called rays. Before using that model, it helps to understand what light is in a basic physical sense. In this chapter, we focus on the nature of light itself, only at the level needed to support the later study of reflection, refraction, mirrors, lenses, and ray diagrams.
Light as electromagnetic radiation
Light is a form of electromagnetic radiation. That means it is part of a broad family that also includes radio waves, microwaves, infrared, ultraviolet, X rays, and gamma rays. What makes visible light special is simply that the human eye can detect it.
Electromagnetic radiation carries energy and can travel through empty space. Unlike sound, it does not need a material medium such as air or water. Sunlight reaches Earth by crossing the nearly empty vacuum of space.
In a vacuum, light travels at a universal speed denoted by $c$:
$$
c \approx 3.00 \times 10^8 \ \text{m/s}
$$
This speed is extremely large, which is why light often seems to arrive instantly in everyday life.
Important fact: Light is electromagnetic radiation and in vacuum it travels at
$$
c = 3.00 \times 10^8 \ \text{m/s}
$$
This value is one of the most important constants in physics.
Visible light
Visible light is only a small part of the electromagnetic spectrum. Different visible colors correspond to different wavelengths, or equivalently, different frequencies. Red light has a longer wavelength than blue light.
A rough visible range is shown below.
| Color | Approximate wavelength |
|---|---|
| Violet | $380$ to $450 \ \text{nm}$ |
| Blue | $450$ to $495 \ \text{nm}$ |
| Green | $495$ to $570 \ \text{nm}$ |
| Yellow | $570$ to $590 \ \text{nm}$ |
| Orange | $590$ to $620 \ \text{nm}$ |
| Red | $620$ to $750 \ \text{nm}$ |
Here, $1 \ \text{nm} = 10^{-9} \ \text{m}$.
Wavelength, frequency, and speed
Light can be described as a wave. For any wave, the speed, wavelength, and frequency are related by
$$
v = f\lambda
$$
For light in vacuum, $v = c$, so
$$
c = f\lambda
$$
where $f$ is the frequency and $\lambda$ is the wavelength.
If the wavelength is shorter, the frequency is higher. If the wavelength is longer, the frequency is lower.
Key relationship for light waves:
$$
v = f\lambda
$$
In vacuum, this becomes
$$
c = f\lambda
$$
Light as rays
In geometrical optics, light is usually represented by rays. A ray is an ideal line showing the direction in which light energy travels. This model works very well when the wavelength of light is much smaller than the size of objects and openings involved.
That is why straight line ray drawings are so useful for mirrors, lenses, shadows, and image formation. Later chapters will use this ray model heavily.
The ray model is an approximation, but it is often an excellent one.
Sources of light
Some objects emit their own light. These are called luminous objects. The Sun, a candle flame, and a light bulb are examples. Other objects are visible because they reflect light from a source. A book on a desk is seen because light from a lamp or the Sun reflects from it into your eyes.
This simple distinction is important in optics because seeing usually involves three parts, a source of light, an object, and an observer.
| Type of object | Meaning | Example |
|---|---|---|
| Luminous | Produces its own light | Sun, LED, flame |
| Illuminated | Seen by reflected light | Moon, wall, book |
Transparent, translucent, and opaque materials
Light interacts with materials in different ways. Some materials let light pass through clearly, some let only part of it through and scatter it, and some block it.
| Material type | What happens to light | Example |
|---|---|---|
| Transparent | Light passes through clearly | Clean glass, water |
| Translucent | Light passes through but is scattered | Frosted glass |
| Opaque | Light does not pass through | Wood, metal |
These categories are very useful in geometrical optics because they help explain image formation, shadows, and visibility.
Rectilinear propagation of light
In a uniform medium, light travels in straight lines. This idea is called rectilinear propagation. It explains common effects such as sharp shadows and the operation of simple pinhole devices.
If an opaque object blocks some rays from a source, a shadow forms behind it because light does not bend around the object significantly in ordinary geometrical situations.
Basic rule of geometrical optics: In a uniform medium, light travels in straight lines.
Light carries energy
Light is not just something we see, it also transports energy. Sunlight warms surfaces, solar panels convert light energy into electrical energy, and concentrated light can heat materials strongly.
Even in geometrical optics, it is useful to remember that rays represent the direction of energy transport.
A first note on wave and particle ideas
At an introductory level, light has a dual nature. In many situations it behaves like a wave, which helps explain wavelength, color, and later topics in wave optics. In other situations it behaves like a collection of particles called photons, which becomes important in modern physics.
For geometrical optics, the ray description is usually enough. Still, it is good to know that the ray model is not the deepest description of light, only a very practical one.
Why the nature of light matters in geometrical optics
The study of geometrical optics relies on a few basic facts about light. It travels extremely fast, it usually moves in straight lines in a uniform medium, it can reflect and refract at boundaries, and it allows us to see objects by emission or reflection.
These ideas are the foundation for the next chapters, where the path of light rays will be used to analyze mirrors, lenses, and optical instruments.