Name: Sign Convention
Uploaded: 2019-07-19
Duration: 7 min 37 s
Description: All distances are measured from the optical centre of the lens. Distances measured in the direction opposite to the incident light's direction are considered...

Question

Define centre of curvature, radius of curvature and aperture of a spherical mirror and obtain the relation between focal length and radius of curvature of a convex mirror

Accepted Answer

With the help of the diagrams(a) and (b) of the spherical mirror drawn above, the following terms are defined.

(i) Centre of the curvature-The centre of the sphere of which the mirror is a part is the centre of curvature. In the figure $C$ is the centre of the curvature.

(ii) Radius of the curvature-The radius of the sphere of which the mirror is a part is the centre of curvature. In the figure $C P$ is the radius of the curvature.

(iii) Aperture-The total length of the reflecting surface is called the aperture of the mirror. In the figure $M_{1} C M_{2}$ is the aperture of the mirror.

Consider the following diagram for the reflection taking place at the concave surface.

As clear $∠ O A C = ∠ A C P (alternate angles)$

also $∠ O A C = ∠ C A F (Law of reflection)$

Since L.H.S. is same, therefore, we have.

$∠ A C P = ∠ C A F$ Which makes $∆ A C F$ Isosceles triangle.

The opposite sides of the equal angles of the isosceles triangles are equal.

So, $C F = F A = F P$

Or, $C P = 2 P F$

Which can be written as $R = 2 f$ , letters have their usual meaning.

Define centre of curvature, radius of curvature and aperture of a spherical mirror and obtain the relation between focal length and radius of curvature of a convex mirror

Important Questions on Reflection of Light : Spherical Mirrors

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