Concave and convex mirrors, and diverging lenses
A concave mirror curves inward, like the inside of a spoon, and reflects parallel light rays so they meet at a focal point. When the object is far from the mirror, it forms a real, upside-down image; when the object is closer than the focal point, it forms an upright, magnified virtual image, which is why makeup and shaving mirrors are concave. Concave mirrors also gather light in many telescopes, and a flashlight or headlight with its bulb at the focal point sends out a strong parallel beam. A convex mirror curves outward and spreads reflected rays apart, so it always forms a smaller, upright, virtual image while showing a wide field of view. That makes it useful for store security mirrors and a car's passenger-side mirror, where objects are closer than they appear. A diverging, or concave, lens is thinner in the middle than at the edges and spreads light rays apart, so it also always forms an upright, smaller, virtual image; diverging lenses in eyeglasses correct nearsightedness. The same equation, 1/f = 1/d_o + 1/d_i, works for all of these, using a negative focal length for convex mirrors and diverging lenses and a negative image distance for virtual images.
This explanation is AI-generated and can occasionally be wrong.
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