   Chapter 25, Problem 62PE

Chapter
Section
Textbook Problem

Use the law of reflection to prove that the focal length of a mirror is hall its radius of curvature. That is, prove that f = R/2. Note this is true for a spherical mirror only if its diameter is small compared with its radius of curvature.

To determine

To Prove:

The focal length of a mirror is half of the radius of curvature by using the law of reflection.

Explanation

Consider a spherical mirror whose ray diagram is given below.

If a ray parallel to the principal axis is incident on a spherical mirror then the angle of incidence will be equal to the angle of reflection. The dotted line in the above diagram represents the perpendicular to the mirror surface at point B.

From above property,

θ1=θ2 ...... (1)

From properties of parallel lines,

θ1=θ3...... (2)

From equation (1) and (2),

θ2=θ3

As θ2=θ3 , ΔACD is an isosceles triangle to ΔBCD

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