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In these revision notes for Mirrors. Equation of Curved Mirrors. Image Formation in Plane and Curved Mirrors, we cover the following key points:
Mirrors are reflecting surfaces used to change the direction of light.
We can divide mirrors in two main categories:
1 - Plane mirrors. In these mirrors, an incident bundle of parallel rays coming from infinity will produce parallel rays even after reflection, as shown in the figure of the previous paragraph.
2 - Curved mirrors. They are formed by a part of a spherical shaped mirror. This category of mirrors contains two sub-categories in itself. They are:
2 a) Concave mirrors, in which only the inner part of the curved reflecting surface is reflective. In concave mirrors, a parallel beam coming from infinity will converge at a single point called focus, which is located at half-distance between the mirror and the geometrical centre of the sphere from which the mirror originates.
2 b) Convex mirrors, in which only the outer part of the curved reflecting surface is reflective. In convex mirrors, a beam of parallel rays coming from infinity will diverge after striking the mirror in such a way that the extension of these rays passes through focus.
The image produced by plane mirrors is laterally inverted. Since this image is obtained by the extensions of reflected rays and not by the reflected rays themselves, it is called "virtual image". Its dimensions are equal to those of the original object and the distance from the mirror is the same as the distance from object to mirror (do = di).
There are four special rays used to build the image in spherical mirrors. They are:
Since in convex mirrors the centre of curvature and focus are on the other side of reflecting surface, there is only a single case of image formation, as there are no divisions on the object's placement side. The image formed by convex mirrors is diminished, it is formed on the other side of the mirror, closer than focus and it is erect (upright). Since the image is not obtained from the reflected rays but from their extensions instead, it is a virtual image.
There is an equation that provides the numerical relationship between the object's distance do, image distance dî and focal length (focus) F, which allows us to determine the position of image without having need for drawings. This equation (known as the Equation of Curved Mirrors) is
We must apply the sign rules to avoid mistakes in calculations. These rules are:
In daily life, magnification M is calculated by dividing the height of the image to the height of the original object. In symbols, we have:
However, applying the triangle similarity rules, we can use another formula for the magnification of curved mirrors. It considers the image and object's position and does not require any information about the height of the object. Thus, we have
If there are two more curved mirrors in the same system, calculations are performed by considering the mirrors one by one. This means the image produced by the first mirror acts like an object for the second mirror and so on. The rules are the same as for a single curved mirror.
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