Relation between focal length and radius of curvature

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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

Relation between focal length and radius of curvature

For Convex Mirror

Relation between focal length and radius of curvature

∠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.

Therefore,

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.

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Manoj Kumar Verma

Hi, I'm Manoj Kumar Verma, a physics faculty having 7 years of teaching experience. I have done B.Tech (E.E.). I am also a YouTuber and Blogger. This blog is dedicated to help students learn the physics concepts easily.

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