Introduction to Ray Optics and Reflection by Spherical Mirrors

What is Light?

Of the entire electromagnetic spectrum, our eyes respond to only a tiny sliver. The human retina can detect electromagnetic radiation with wavelengths between roughly 400 nm (violet) and 750 nm (red). This narrow band is what we call light, and it is the primary way we observe and make sense of the world around us.

Two facts about light stand out from everyday experience:

• Light is incredibly fast. Its speed in vacuum is $c = 2.99792458 \times 10^8$ m/s, often rounded to $c = 3 \times 10^8$ m/s. This is the fastest anything can travel in nature; no material object or signal can exceed this limit.
• Light appears to travel in straight lines. Shadows have sharp edges, and you can block a light source by holding an object in front of it. This everyday observation is what allows us to use the ray model of light.

Why Does the Ray Model Work?

You might wonder: if light is actually an electromagnetic wave, how can we say it travels in straight lines? The answer lies in scale. The wavelength of visible light (a few hundred nanometres) is extremely small compared to the size of objects we normally deal with (a few centimetres or larger). When the wavelength is much smaller than the object it encounters, wave effects like diffraction (the spreading of waves around obstacles, causing them to bend around edges) become negligible. Under these conditions, light travels from one point to another along a straight-line path.

This straight-line path is called a ray of light. A collection of rays bundled together is called a beam of light. The study of light using this straight-line ray picture is known as ray optics or geometrical optics. It covers reflection, refraction, dispersion, and image formation by mirrors and lenses.

The Laws of Reflection: How Light Bounces Off Surfaces

When a ray of light strikes a surface, part of it bounces back. The rules governing this process are called the laws of reflection, and they hold at every point on any reflecting surface, whether flat or curved.

Fig 9.1: The incident ray, reflected ray, and the normal to the reflecting surface lie in the same plane

There are two laws:

1. The angle of incidence equals the angle of reflection. The angle of incidence is measured between the incoming ray and the normal (a line perpendicular to the surface at the point where the ray hits). The angle of reflection is measured the same way, between the outgoing ray and the normal. These two angles are always equal.

2. The incident ray, the reflected ray, and the normal all lie in the same plane. This is the coplanarity condition. You can visualise it as all three lines sitting flat on the same sheet of paper.

These two laws are universal. They apply to plane mirrors, curved mirrors, and even rough surfaces (at each tiny point on the surface, the laws still hold locally).

Spherical Mirrors: Key Terminology

A spherical mirror is a mirror whose reflecting surface is a part of a sphere. Before studying how these mirrors form images, it helps to get familiar with the basic terms used to describe them.

• Pole (P): The geometric centre of the mirror’s reflecting surface. Think of it as the midpoint of the mirror.

• Centre of curvature (C): The centre of the sphere from which the mirror is cut. Every point on the mirror surface is equidistant from this centre.

• Principal axis: The straight line that passes through both the pole and the centre of curvature. This is the reference line for describing ray paths and image positions.

• Normal at any point: For a spherical mirror, the normal at any point on the surface lies along the radius of the sphere at that point. In other words, it is the line joining the centre of curvature to the point where the ray strikes the mirror. When applying the laws of reflection to a curved mirror, this is the normal you use.

There is a parallel set of terms for lenses. The geometric centre of a spherical lens is called the optical centre (not the pole), and the principal axis of a lens connects the optical centre to its principal focus (rather than to the centre of curvature).

These definitions form the vocabulary you will use throughout this chapter as you study image formation by mirrors and lenses.