Perhaps when you hear the word "mirror," you think of an ordinary flat surface; this kind is most suitable for gazing at your own reflection because it doesn't distort reflected images. In the scientific world, however, convex -- or outwardly curved -- and concave -- or inwardly curved -- mirrors are more typical, with myriad applications in engineering and technology.
Galileo Galilei invented the first astronomical telescope in 1609, leading to the controversial discovery that Earth revolves around the sun and not vice versa. Today, two types of telescopes are widely used: refractor telescopes, which employ lenses, and reflector telescopes, which have mirrors. In a reflector telescope, light from the object of interest enters the far end of the telescope and strikes a concave mirror at the end closest to the viewer. The reflected light rays are convergent and meet at a focal point, where a plane mirror then reflects the image to the eyepiece. As technology has improved over the years, these devices have become increasingly powerful.
Driving a car without being able to know what's going on behind you would be a hazardous endeavor indeed. Thanks to the optical properties of convex mirrors, motorists have a buffer against all manner of dangers. Both side-view and rear-view mirrors are convex, which means that the image focal point is actually behind the mirrors and the reflected rays spread outward. The expanded field of view results in the smaller-than-real-life image you see -- hence the typical warning "Objects in mirror are closer than they appear."
The Satellite Dish
Satellite dishes for residential television reception are virtually ubiquitous in the 21st century, and they have important commercial and military applications. Although the electromagnetic waves reaching these structures from orbiting satellites lie outside the visible spectrum, the satellite dish is nonetheless a concave mirror. The virtually parallel waves are reflected to a receiver at a focal point in front of the dish and are then translated into a visual or other practical signal that is greatly amplified thanks to the concentration of the waves at a small locus.
As the name implies, a solar cooker uses energy from the sun to heat foot. These take advantage of a convex or parabolic mirror constructed from a metal such as aluminum foil. Equations from geometry allow makers of these ovens, from commercial entities to schoolchildren taking part in science fairs, to calculate exactly where the focal point of the oven lies and therefore where the food must be placed. As with a satellite dish, the energy from the radiation, in this case solar energy, is concentrated within a small space and is thus very efficient at heating food.