Chapter 25: Q62PE (page 932)

Use the law of reflection to prove that the focal length of a mirror is half 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.

Short Answer

Expert verified

Through plotting the image, it is proved that the focal length of a mirror is half its radius of curvature.

Step by step solution

Concept Introduction

When light incidents on a surface and the surface relects it, the angle of incidence equals the angle of reflection, according to the law of reflection.

Plotting the diagram

Plot an image that shows an incident ray parallel to the principal axis.

Calculation for focal length

The angle of incidence equals the angle of reflection –

$α = β$

Using the properties of parallel lines –

$α = γ$

Therefore, it can be obtained –

$α = β = γ$

Hence, the $∆ CDF$ is congruent to the triangle $∆ BDF$ .

Since $α = γ$ , $CP$ is the radius of curvature $R$ .

$CB = CP$

$CB = R$

Also, it can be observed that –

$CD = \frac{CD}{2} And CF = CD$

So, now we get that –

$CP ‐ CF = f$

Substituting values in the above equation, we get,

$R ‐ \frac{R}{2} = f f = \frac{R}{2}$

Hence, proved that the focal length of a mirror is half its radius of curvature.

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Use the law of reflection to prove that the focal length of a mirror is half 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.

Short Answer

Step by step solution

Concept Introduction

Plotting the diagram

Calculation for focal length

One App. One Place for Learning.

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Use the law of reflection to prove that the focal length of a mirror is half 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.

Short Answer

Step by step solution

Concept Introduction

Plotting the diagram

Calculation for focal length

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Quantum Physics

Measurements

Electromagnetism

Space Physics

Particle Model of Matter

Medical Physics

Study anywhere. Anytime. Across all devices.

Use the law of reflection to prove that the focal length of a mirror is half 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.