The Nature of Light

Light is an electromagnetic wave — a coupled oscillation of electric and magnetic fields that propagates through space without requiring a medium. In a vacuum all electromagnetic waves travel at the same constant speed:

$$c = 3 \times 10^8\ \text{m/s}$$

(More precisely, $c = 2.998 \times 10^{8}\ \text{m/s}$.) This is one of the fundamental constants of nature. When light enters a material medium (glass, water, air), it slows down. The ratio of the speed of light in a vacuum to its speed $v$ in a given medium is called the refractive index of that medium:

$$n = \frac{c}{v}$$

For example, glass has a refractive index of approximately 1.5, meaning light travels at $c/1.5 \approx 2 \times 10^8\ \text{m/s}$ inside glass. Air has $n \approx 1.00$, so light only barely slows in air relative to a vacuum.

The Law of Reflection

When a ray of light strikes a smooth surface (a mirror) it bounces back. Angles are always measured from the normal — the imaginary line perpendicular to the surface at the point of incidence. The law of reflection states:

> The angle of incidence equals the angle of reflection.

$$\theta_i = \theta_r$$

where $\theta_i$ is the angle between the incoming ray and the normal, and $\theta_r$ is the angle between the reflected ray and the normal. Both angles lie in the same plane as the normal.

Specular vs. diffuse reflection: A polished mirror gives specular (regular) reflection — parallel rays remain parallel after reflection, producing a clear image. A rough surface gives diffuse reflection — parallel rays scatter in many directions because the normal direction varies across the surface, so no clear image is formed.

Refraction and Snell's Law

Refraction occurs when light passes from one transparent medium into another and changes speed, causing the ray to bend at the boundary. The bending happens because one edge of the wavefront slows (or speeds up) before the other.

• Light going from a less dense to a more dense medium (e.g., air to glass) slows down and bends towards the normal.
• Light going from a more dense to a less dense medium (e.g., glass to air) speeds up and bends away from the normal.

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

$$n_1 \sin\theta_1 = n_2 \sin\theta_2$$

where $n_1$ and $\theta_1$ are the refractive index and angle of incidence in the first medium, and $n_2$ and $\theta_2$ are those in the second medium.

Worked example: A ray passes from air ($n_1 = 1.00$) into glass ($n_2 = 1.50$) at an angle of incidence of 45° ($\sin 45° \approx 0.707$).

$$\sin\theta_2 = \frac{n_1 \sin\theta_1}{n_2} = \frac{1.00 \times 0.707}{1.50} = 0.471 \qquad \Rightarrow \qquad \theta_2 = \arcsin(0.471) \approx 28.1°$$

The refracted ray is closer to the normal (28.1° < 45°), confirming that light bends towards the normal entering the denser medium.