**Relation between radius of curvature (R) and focal length (f)**

**In Concave Mirror**

Consider a concave mirror of a small aperture. When a ray of light OA parallel to principal axis is incident at point A on the mirror, it will be reflected along AB passing through the focus F as shown in the figure. Join AC which is normal at A.

From the laws of reflection of light,

And

[Due to alternate angle.

Hence ΔACF is an isosceles triangle and in such triangle AF = FC ……….. (iii)

If the aperture of the mirror is small, then points A and P are very close to each other, and we will have AF nearly equal to PF.

Thus, Eq.(iii) becomes

PF = FC

or PF = PC – PF

Or, 2PF = PC

Or, 2f = R

Or, f = R/2

**In Convex mirror**

Consider a convex mirror of focal length f and small aperture. A ray of light OA parallel to the principal axis is incident at point A on the mirror and it passes along AB after reflection as shown in figure. The virtual image will be formed at F int the next side of the object. Join CA and produce outward. Here C is the center of curvature and P is the pole of mirror.

From equation (i) and (ii), we have,

Hence, ΔACF is an isosceles triangle. So,

AF = FC ………. (v)

If the aperture of the mirror is small, then points A and P will lie very close to each other. So, AF = PF and Equation (v) becomes

PF = FC = PC – PF

2PF = PC

2f = R

F = R / 2

**Parabolic Mirror**

A mirror which has a reflecting surface in the shape of parabola is called the parabolic mirror.

**Magnification**

It is defined as the ratio of the size of image performed by the spherical mirror to the size of the object. It is denoted by m.

m = size of image / size of object

= v / u

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