Why study curved mirrors?

Light carries information about where things are, and energy. To concentrate the information (to make distant galaxies visible) or the energy (to get sunlight to boil water to run a turbine) involves redirecting it, which can be done with a lens or a curved mirror. Curved mirrors are simpler: their effect can be understood in terms of geometry.

Curved mirrors are used to make the very best telescopes, because the mirror treats all wavelengths of light the same. Large telescopes on earth (like Palomar) and the Hubble Space Telescope are based on curved mirrors. A TV satellite dish is also a curved mirror, that focuses radio waves onto a detector.

Convex mirrors are used to give wide-angle view at awkward corners and in a car's passenger-side rear-view mirror.

Examples of curved mirrors
a light beam encounters a reflecting ring A ring-shaped cookie cutter in a light beam
Light hitting the inside is focussed
Light hitting the outside is made to diverge

Convex mirrors for looking around corners

These mirrors have been placed along a busy road, so that people trying to enter it from another road can clearly see both ways.

A reflection in a car windshield

A tree is reflected in the window of the car.

Sunlight reflected from car windows The windshield of this car is a curved mirror, that produces a virtual image of the sun. It's still too bright to look at!
A TV screen reflects the scene outside The curved TV screen distorts the world reflected in it
(A metaphor? No, just an observation...)
We can see transparent objects because they reflect some light from their surfaces. Here some water spilled on a counter top reveals its shape by the way it reflects the view out the window behind it. (The reflected view is upside down. The green blur is a tree, somewhat out of focus.)

We usually ignore the reflections we see in curved mirrors, because they are so distorted that we can't interpret them. The result is that we don't realize how prevalent they are.
A post in a lake, reflected in the wavy water surface Waves on a lake reflect the sky and the shore

Curved objects that are made of reflecting materials are all around us. In this picture you can see the reflection of the window on the bottle, and the photographer (both right-side up and upside-down) reflected in the spoons.

Shiny spoons and platters reflect their surroundings