The law of reflection states that the angle of incidence equals the angle of reflection. Both angles are measured from the normal line, which is an imaginary line drawn perpendicular to the surface at the point where the light hits. The incident ray (incoming light), the reflected ray (outgoing light), and the normal all lie in the same plane.

Think of it like a ball bouncing off a wall: the angle going in matches the angle going out.

Types of Reflection

Not all surfaces reflect light the same way. The difference comes down to smoothness.

Specular reflection occurs on smooth surfaces like mirrors or calm water. The reflected rays stay parallel to each other, producing a clear image.
Diffuse reflection occurs on rough surfaces like paper, clothing, or an unpolished wall. The surface has tiny irregularities, so reflected rays scatter in many directions. You can still see the object, but you don't get a mirror-like image.

Most real-world surfaces produce a combination of both. A glossy magazine page, for example, is smoother than notebook paper but rougher than a mirror.

Principles of Reflection, 24.1: Overview - Physics LibreTexts

Applications of Reflection

Mirrors rely on specular reflection to produce clear images (flat mirrors in bathrooms, curved mirrors in telescopes).
Retroreflectors on road signs and bike reflectors use multiple angled surfaces to bounce light directly back toward its source, making them visible at night.
Solar cookers use curved reflective surfaces to concentrate sunlight onto a small area, generating enough heat to cook food.
Reflecting telescopes use large curved mirrors to gather light from distant stars and galaxies, then focus it for observation.
Fiber optic cables keep light trapped inside using a special case of reflection called total internal reflection (covered below).

Refraction

Principles of Reflection, 25.2 The Law of Reflection – College Physics

Fundamentals of Refraction

Refraction is the bending of light as it passes from one material into another. It happens because light changes speed when it enters a new medium.

The index of refraction ( $n$ ) tells you how much a material slows light down compared to its speed in a vacuum:

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

Here, $c$ is the speed of light in a vacuum (about $3 \times 10^8$ m/s) and $v$ is the speed of light in the material. A higher index means light travels slower in that material. For reference: air has $n \approx 1.00$ , water has $n \approx 1.33$ , and glass is roughly $n \approx 1.50$ .

Snell's Law connects the angles and indices of refraction on each side of the boundary:

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

where $\theta_1$ is the angle of incidence and $\theta_2$ is the angle of refraction, both measured from the normal.

Behavior of Light During Refraction

Two key rules to remember:

Light bends toward the normal when it enters a denser (higher $n$ ) medium. For example, a beam of light going from air into water bends toward the normal because water's index is higher.
Light bends away from the normal when it enters a less dense (lower $n$ ) medium. A beam going from water into air bends away from the normal.

This bending creates some familiar effects:

Apparent depth: A swimming pool looks shallower than it really is because light bending at the water-air boundary makes the bottom appear closer to the surface.
Dispersion: Different colors of light bend by slightly different amounts. When white light enters a prism, it separates into a spectrum of colors (red bends least, violet bends most) because each color has a slightly different speed in glass.
Rainbows form when sunlight enters water droplets, refracts, reflects off the back of the droplet, and refracts again on the way out. The dispersion during these refractions spreads the colors across the sky.

Total Internal Reflection

When light tries to pass from a denser medium into a less dense one (like from water into air), something special can happen. If the angle of incidence is large enough, the light doesn't pass through at all. Instead, it reflects completely back into the denser medium. This is total internal reflection.

The critical angle ( $\theta_c$ ) is the smallest angle at which total internal reflection occurs. You can calculate it with:

$\sin \theta_c = \frac{n_2}{n_1}$

where $n_1$ is the denser medium and $n_2$ is the less dense medium (so $n_1 > n_2$ ). At any angle of incidence greater than $\theta_c$ , all the light reflects back; none passes through the boundary.

Fiber optics rely on this principle. Light enters a thin glass or plastic fiber and hits the walls at angles above the critical angle, so it bounces along the entire length of the cable with very little loss. This is how internet data travels at high speeds over long distances.
Diamonds have a very high index of refraction ( $n \approx 2.42$ ), which gives them a small critical angle. Light entering a diamond gets trapped inside through repeated total internal reflections before finally escaping, which is what creates that intense sparkle.

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