Universal mirrors
The make-up mirror magnifies a face viewed from a short distance and the car rear-view mirror de-magnifies the objects viewed. One of them is concave while the other is convex. Mirrors used for the make-up magnify the image only when they are held close to your face. In contrast to concave mirrors, the image in the convex mirror (the road one) is always straight (and then virtual and de-magnified). This is the same as in concave (de-focusing) glasses used by short-sighted persons.
The image in a concave mirror may be straight or reversed, depending on the distance from the mirror to the object. In the example below, the object is positioned between the mirror and its focal point. In such a case the image is virtual, magnified and straight.
The following equation describes the relation between the distance of the object p and the image q from the mirror on one hand and the focal point f on the other.
In case of the convex mirror the relation in question looks similarly, with the exception of focus, which has a negative value. In the convex mirror the image is created on the 'other' side of it (q < 0), therefore it is always virtual.
The big concave mirror in the Hubble Space Telescope is used to view distant galaxies. The Hubble Space Telescope is an example of the refracting telescope in Cassegrain system (Cassegrain telescope has the parabolic primary mirror and a smaller secondary elliptical one, directing the light through the perforated primary mirror into an eyepiece). Telescopes in this system have lower brightness, which makes them particularly useful for viewing brighter objects such as the moon and planets.
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Big diameter focusing mirrors enable to see objects of lesser brightness. The mirrors with which Archimedes deterred the Romans were plane or concave. ones.
To cut a long story short - (spherical) mirrors serve many purposes.