Reflection

Waves bounce off a surface at the same angle they strike it:

Incident ray and reflected ray with equal angles on either side of the normal line

Angle In Matches Angle Out

Or in more mathematical language:

Angle of Incidence = Angle of Reflection
The Law of Reflection

Another example:

Ray hitting a flat surface at a shallow angle and reflecting away at the same angle

Horizontal surface line with a vertical normal line marked with a 90-degree square

The Normal is the direction directly away from the surface (at right angles to it).

Angles are measured from the Normal.

Mirror

Here we see light bouncing off a mirror to create a "virtual image" that looks like the real thing (but reversed):

Puppy looking into a plane mirror seeing an upright virtual reflection behind the mirror
Our puppy sees someone in the mirror.

Curved Mirrors

What happens when light reflects off a curved surface? We can draw individual rays of light to discover!

Here's how to work out the reflection of a ray:

Curved line with a flat tangent line drawn where a light ray strikes

Where the ray hits draw a line flat against the curve (called a tangent line)

Dashed normal line drawn at a right angle to the tangent line on a curve

The normal line is at right angles to that tangent line

Reflected ray drawn with an angle matching the incident ray across the normal line

Angle In matches Angle Out either side of the normal line

And we get this:

Concave curved mirror reflecting light rays to form an inverted image of a puppy
Our puppy sees an upside down reflection!

Just like the inside of this spoon:
Inverted reflection of a person seen inside the bowl of a metal spoon

Try it with a shiny spoon:

Look into the inside of the spoon (curved inward like a cave, or concave): what do you see?
Try the back of the spoon (curved outward, or convex): what do you see now?

And what about this wonderful shape:

Curved metallic Cloud Gate sculpture reflecting Chicago buildings and blue sky
Cloud Gate in Chicago

Parabola

The parabola is a special curved shape that takes any ray coming directly in and sends it to a single "focus" point:

Parallel incoming rays bouncing off a parabolic curve and meeting at one focal point

This is useful for telescopes. They can have a large parabolic collection area that sends the radiation to one small detector.

Technicians in cleanroom suits standing in front of a gold hexagonal mirror segment
Technicians stand in front of one segment of the James Webb Telescope's
"segmented parabolic reflector"

Dish antenna of the Plateau de Bure radio telescope pointing upward
Incoming radio waves get sent to the focal point for detection.
Plateau de Bure Radio Telescope

Ellipse

For an ellipse, light or sound starting at one focus point reflects to the other focus point:

Rays starting at one ellipse focus reflecting off the perimeter to converge at the second focus

Have a play with a simple computer model of reflection inside an ellipse.

Echo

An echo is a reflection, usually of sound from a hard surface.

Sound waves traveling from clapping hands to ears directly and reflecting off a wall
As well as hearing it directly, the sound of this clap
is also heard a short while later from the wall

Other types of waves can have echoes, such as radio waves.

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