Reflection and Refraction Explained: Mirrors and Snell’s Law

Light as rays

For most everyday optics we treat light as rays: straight lines with an arrow showing the direction light travels. This ray model works well when objects are much larger than the wavelength of light, which covers mirrors, lenses and ordinary shadows. It ignores wave effects like diffraction, so it is an approximation, but a very useful one.

One idea keeps every diagram honest. Angles are measured from the normal, an imaginary line at right angles to the surface at the point where the ray lands. Measuring from the surface itself instead is the most common way to get a wrong answer.

The law of reflection

When a ray strikes a smooth surface, it bounces off at the same angle it arrived at:

θᵢ = θᵣ

The incoming ray, the outgoing ray and the normal all lie in one flat plane. That is the whole law, and it is exact for a smooth mirror.

What a flat mirror does to an image

A plane mirror forms a virtual image. Your eye traces the reflected rays backwards in straight lines and finds they seem to come from a point behind the mirror, as far behind as the object is in front. No light actually arrives from there, which is why you cannot project that image onto a screen.

The image is the same size as the object, but flipped front to back, so your right hand looks like the left hand of your double. Chain two mirrors at the right angles and you get a periscope: each mirror obeys the same law, and together they steer light around a wall.

Why light bends: refractive index

Light travels fastest in a vacuum, about 300,000 km/s. In a material like water or glass it moves more slowly. The refractive index n compares the two:

n = c / v

Air is very close to 1, water is about 1.33, ordinary glass about 1.5, and diamond is above 2. A bigger n means a slower light speed and a stronger bending.

When a ray crosses at an angle from one material into another, one side of the beam slows down before the other, and the beam turns. That is refraction. Part of the light is reflected at the same boundary, so a window both lets you see through and shows a faint reflection.

Snell’s law

The exact rule for refraction is Snell’s law:

n₁ sin θ₁ = n₂ sin θ₂

Each angle is measured from the normal, in its own material. Suppose light goes from air (n about 1.00) into water (n about 1.33) at 45°. Then sin θ₂ = sin 45° ÷ 1.33, which is about 0.53, giving an angle near 32°. The ray has bent closer to the normal.

Toward or away from the normal?

You do not need to calculate to know the direction:

• entering a denser material (higher n), the ray bends toward the normal;
• entering a rarer material (lower n), it bends away.

The paths are reversible, so a ray going back out follows the same route in reverse. If the angle in the denser material gets large enough, light leaving it cannot refract at all and reflects completely instead, an effect called total internal reflection that fibre optics rely on.

Everyday refraction

Refraction explains several familiar illusions:

• A pool looks shallower than it is. Light leaving the water bends away from the normal, so the bottom seems raised. Looking nearly straight down, apparent depth is about the real depth divided by n.
• A straw looks broken at the water's surface because the part below is seen through bent light.
• A coin hidden behind a cup's rim can appear when you add water, because the rays now bend over the edge.
• A road mirage is not a puddle at all. Light from the sky bends upward through layers of hot, thinner air and reaches your eye from below.

Notice that all of these are the same Snell's law, just applied in different places.

Common misconceptions

• "Light slows down because it hits atoms and stops." The wave is delayed as it travels through the material; once it leaves, it returns to full speed.
• "A mirror reverses left and right." It reverses front and back; your left-right confusion comes from how you imagine turning around.
• "Bending depends on the thickness of glass." It depends on the angle and the two refractive indices, not on thickness, which only shifts a ray sideways.
• "A virtual image is imaginary." It is just a point the light appears to come from. Your eye sees it perfectly well.

How to explore this in the lab

The Light & Optics lab lets you aim real rays at mirrors and glass blocks and measure the angles. A path through the free first world:

1. Verify the bounce rule in The Law of Reflection.
2. See the hidden image in Plane Mirrors & Images.
3. Slow the light in Refractive Index, then use Snell's Law.
4. Predict directions in Toward or Away from the Normal, then explain pools in Apparent Depth.

The lab is a simplified teaching model with ideal flat surfaces and a single wavelength of light, so the numbers come out cleanly. Real glass spreads colours slightly, which is a story for the later worlds.