Relation between focal length and radius of curvature
(f = R/2)
Relation between focal length and radius of curvature :- Let C be the center of curvature of the mirror. Consider a ray parallel to the principal axis striking the mirror at M. Then CM will be perpendicular to the mirror at M. Let θ be the angle of incidence, and MD be the perpendicular from M on the principal axis. Then,
For Concave Mirror
For Convex Mirror
∠MCP = θ and ∠MFP = 2θ
tanθ = MD/CD and tan 2θ = MD/FD
For small θ, which is true for paraxial rays, tanθ ≈ θ and tan 2θ ≈ 2θ.
MD/FD = 2(MD/CD)
Or FD = CD/2
Now, for small values of θ, the point D is very close to the point P. Therefore, FD = f and CD = R. Then
f = R/2
Next Topic :- Mirror Formula.