1. What Is Geometrical Optics?

Geometrical optics is one of the most intuitive and fundamental branches of optics. Instead of treating light as a complex electromagnetic wave, it simplifies light into “rays.” These rays travel in straight lines, reflect from mirrors, and refract when entering different media. Because this model is simple and powerful, it helps us explain many familiar phenomena: Why do mirrors form images? Why does a chopstick look bent in water? How does a magnifying glass enlarge text? How does a camera lens create a sharp photograph?

2. Rectilinear Propagation of Light

In a uniform medium, light generally travels in straight lines. This principle explains how shadows form. When sunlight reaches an object, the object blocks part of the light, creating a shadow behind it. Solar and lunar eclipses can also be explained through similar geometry: when the Sun, Earth, and Moon align in particular ways, one celestial body blocks light from reaching another.

A “ray” in geometrical optics is not a physical thread of light that can be isolated in reality. It is an idealized tool representing the direction in which light energy travels. Just as a route on a map is not the road itself but helps us understand spatial relationships, the ray model helps us analyze the path of light.

3. Reflection: Why Do Mirrors Form Images?

光遇到光滑表面时会发生反射。反射最核心的规律是：入射角等于反射角。也就是说，光线射向镜面时，与法线形成的角度，等于它反射离开镜面时与法线形成的角度。

When light hits a smooth surface, reflection occurs. The central law of reflection is: the angle of incidence equals the angle of reflection. In other words, the angle between the incoming ray and the normal line equals the angle between the reflected ray and the normal line.

The image in a plane mirror appears to be behind the mirror, but it is actually a visual interpretation formed by tracing reflected rays backward. The mirror does not create a real object behind it. Instead, it reflects light in such a way that our brain interprets the light as coming from a point behind the mirror. This is called a “virtual image.”

Concave and convex mirrors are even more interesting. A concave mirror can converge light rays, making it useful for focusing light, forming images, and building telescopes. A convex mirror spreads light rays outward, so it is often used in car side mirrors and road safety mirrors because it provides a wider field of view.

4. Refraction: Why Does Light Bend?

When light passes from one medium into another, such as from air into water or glass, its speed changes. This change in speed causes the light ray to bend, a phenomenon known as refraction. A chopstick partly immersed in water appears bent because the light coming from it refracts at the water’s surface.

Refraction is described by Snell’s law. In simple terms, when light enters a medium with a higher refractive index, it usually bends toward the normal line. When it enters a medium with a lower refractive index, it bends away from the normal. Lenses, prisms, eyeglasses, and microscopes all depend on refraction.

5. Lenses and Image Formation

Lenses are among the most important tools in geometrical optics. A convex lens is thicker in the middle and thinner at the edges, causing parallel light rays to converge at a focal point. A concave lens is thinner in the middle and thicker at the edges, causing light rays to diverge. A magnifying glass is a convex lens. When an object is placed close to it, the eye sees an enlarged virtual image.

Cameras, projectors, and the human eye can all be considered imaging systems. A camera lens focuses light from a scene onto an image sensor. A projector enlarges a small image and casts it onto a screen. The crystalline lens in the human eye adjusts its focal length so that light focuses on the retina. If the focus falls in front of or behind the retina, nearsightedness or farsightedness occurs, and corrective lenses are needed.

6. Applications of Geometrical Optics

Geometrical optics has a wide range of applications. In medicine, endoscopes use lenses and optical fibers to help doctors observe inside the human body. In communication, optical fibers transmit information through total internal reflection. In astronomy, telescopes collect faint light from distant celestial objects. In daily life, eyeglasses, cameras, headlights, projectors, and smartphone cameras all rely on geometrical optical design.

Modern smartphone cameras are especially impressive. A tiny camera module contains a complex optical structure. Multiple lens elements work together to correct aberrations, making image edges sharper, colors more accurate, and distortion smaller. Geometrical optics not only explains phenomena but also guides engineering design.

7. The Limits of Geometrical Optics

Although geometrical optics is extremely useful, it cannot explain every optical phenomenon. When light passes through a very narrow slit, diffraction occurs. When two beams of light meet, interference may appear. Polarization also requires wave optics for a full explanation. Therefore, geometrical optics is most suitable when the objects involved are much larger than the wavelength of light.

In other words, geometrical optics is like a simplified map, while wave optics and electromagnetic theory are more detailed terrain maps. Different models are useful for different problems, and scientific understanding often depends on choosing the right model.

Conclusion

Geometrical optics uses a simple ray model to make complex optical phenomena easier to understand. Starting from straight-line propagation, reflection, and refraction, it explains how mirrors, lenses, eyes, cameras, and telescopes work. It is not the whole story of optics, but it is the first doorway into the world of light.