Transverse linear increase

In physics, we define a spherical mirror as any polished spherical cap that is capable of reflecting light both inside and outside. In our daily lives we can find different types of mirrors, among them are spherical mirrors. Examples of spherical mirrors are rear view mirrors and mirrors for telescopes.

We know that it is possible to construct the conjugated image by a given spherical mirror, for that we just have to obey the laws of reflection. In the Gaussian frame of reference, that is, in the Cartezian frame of reference that makes the axis of the abscissa coincide with the main axis of the mirror; the axis of the ordinates with the mirror and the origin coincides with the vertex of the mirror, let’s suppose that the i are the ordinates of the extremes A and A’ of the object and the image.

o and i are the measurements of the dimensions of the object and the image. We can see that the sign of o will be positive and i will be negative because the image is inverted. For this situation, if we make the quotient between image and object, we will have a negative final value, therefore, the image will be inverted in relation to the object.

We call linear increase or simply amplification the quotient between the image ( i ) and the object ( o ). If we take as a basis for calculations the similarity of triangles existing between triangles ABV and A’B’V in the figure above, we will have:

Since A’B’ = i , AB = o , VB’ = p’ and VB = p , to maintain sign conventions, we write:

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