Relation between Radius of Curvature (R) and Focal Length (f) | Physics Grade XI

Radius of Curvature (R) and Focal Length (f)

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Relation between Radius of Curvature (R) and Focal Length (f) | Physics Grade XI

Relation between Radius of Curvature (R) and Focal Length (f)

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.

Relation betwee R and f in concave mirror

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.
Relation between R and f in convex 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.
Parabolic MirrorMagnification
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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