Focal length (f) and Radius of Curvature (R) Relation

In this post, we will derive the relation between the Focal Length and Radius of Curvature for convex and concave mirrors. This derivation is important for the class 10th exam.

Relation Between Focal length and Radius of Curvature

For Concave Mirror:

From △ MCN = Tan i = Perpendicular/ Base
Tan i = MN/CN CN = -R (Distance Between Center of Curvature and Pole)
Tan i = MN/-R
Tan i ~ i So,
i = MN/-R – (i)

From △ MFN = Tan 2i = Perpendicular/ Base
Tan 2i = MN/FN
Tan 2i = MN/-f FN = -f (Distance between pole and focus)
Tan 2i ~ 2i So,
2i = MN/-f -(ii)
Putting the value of i in equation 2nd

2 x MN/-R = MN/-f
f = R/2 Hence Proved

For Convex Mirror:

From △ MCN = Tan i = Perpendicular/ Base
Tan i = MN/CN CN = R (Distance Between Center of Curvature and Pole)
Tan i = MN/-R
Tan i ~ i So,
i = MN/R – (i)

From △ MFN = Tan 2i = Perpendicular/ Base
Tan 2i = MN/FN
Tan 2i = MN/-f FN = f (Distance between pole and focus)
Tan 2i ~ 2i So,
2i = MN/f -(ii)
Putting the value of i in equation 2nd

2 x MN/R = MN/f
f = R/2 Hence Proved

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