Question

prove that focal length=Radius of curvature/2​

Answer 1

Answer:

Proving the focal length is half the radius of curvature:

Now the angle between the radius of curvature and principal axis will be equal to the angle at which ray is incident and due to reflections law incident angle would be equal to angle cbf. Hence, in both cases Radius is double the focal length.

Explanation:

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Answer 2

Focal length and radius of curvature:

Let F be focus and C be center of curvature of a concave mirror.

Consider an incident ray travelling parallel to principle axis and meet at point N.

It passes through focus after reflection.

CN is the normal drawn to the mirror(normals drawn to mirror meet at C).

Now,

PC = R

PF = f

∠FNC = ∠FCN =

∠MFN = 2

In ΔMNC

[For paraxial rays, M and P coincide]

If is small,

------------------------(1)

In ΔMNF

[For paraxial rays, M and P coincide]

If is small,

------------------------(2)

Substituting (1) in (2), we get

2PF = PC

R = 2f

f = R/2

Therefore, focal length is half the radius of curvature.

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