Acids, Bases And Salts

Question

Establish the relationship between object distance u, image distance v and radius of curvature f for a convex mirror.

Solution

Mirror formula for a convex mirror:

Consider a convex mirror of small aperture where we assume, P be the pole, F the principal focus and C the centre of curvature.

Let PF = f be the focal length and PC = R be the radius of curvature of the mirror.
Here, AB is an object placed in front of the mirror perpendicular to its principal axis.
A' B' is the virtual, erect image of the object AB formed (behind the mirror) after reflection at the convex mirror.

Fig. Image formed by a convex mirror

Using the new cartesian sign convention, we have

Object distance, BP = - u
Image distance, PB' = + v
Focal length, FP = +f
Radius of curvature, PC = + R = +2f

Now,

∆ A' B' C ~ ∆ ABC

\frac{A' B'}{AB} = \frac{B' C}{BC} = \frac{PC - PB'}{BP + PC} = \frac{2 f - v}{- u + 2 f}

...(1)

As

∠ A' B' P = ∠ BPQ = ∠ APB

Therefore,

∆ A' B' P ~ ∆ ABP .

Consequently,

\frac{A' B'}{AB} = \frac{PB'}{BP} = \frac{ν}{- u}

...(2)

From equations (1) and (2), we get

\frac{2 f - ν}{- u + 2 f} = \frac{ν}{- u}

\Rightarrow

- 2 uf + uv = - uv + 2 νf

\Rightarrow

uν = νf + uf

Dividing both sides by uvf, we get

\frac{1}{f} = \frac{1}{u} + \frac{1}{v}

\Rightarrow

\frac{2}{R} = \frac{1}{u} + \frac{1}{v}

which is the required mirror formula for a convex mirror.

Some More Questions From Acids, Bases and Salts Chapter

What do you mean by reflection, refraction and absorption of light?

Which type of phenomenon (reflection or refraction) occurs when light falls on (i) a highly polished surface like a mirror and (ii) a transparent medium like glass or water?

Define the following terms in connection with reflection of light:
Incident ray, reflected ray, point of incidence, normal, angle of incidence and angle of reflection.

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Acids, Bases And Salts

Establish the relationship between object distance u, image distance v and radius of curvature f for a convex mirror.

Some More Questions From Acids, Bases and Salts Chapter

What do you mean by reflection, refraction and absorption of light?

Which type of phenomenon (reflection or refraction) occurs when light falls on (i) a highly polished surface like a mirror and (ii) a transparent medium like glass or water?

What is meant by the optical image of an object?

What are real and virtual images? Can these images be obtained on a screen? Give reasons in support of your answer.

Give three points of differences between real and virtual images.

What is a mirror? Mention the different types of mirrors commonly used.

Define the following terms in connection with reflection of light:
Incident ray, reflected ray, point of incidence, normal, angle of incidence and angle of reflection.

State the laws of reflection of light.

Are the laws of reflection applicable to plane surfaces also valid for curved surfaces?

State the important properties of images formed by plane mirrors.

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For Daily Free Study Material Join wiredfaculty

Acids, Bases And Salts

Establish the relationship between object distance u, image distance v and radius of curvature f for a convex mirror.

Some More Questions From Acids, Bases and Salts Chapter

What do you mean by reflection, refraction and absorption of light?

Which type of phenomenon (reflection or refraction) occurs when light falls on (i) a highly polished surface like a mirror and (ii) a transparent medium like glass or water?

What is meant by the optical image of an object?

What are real and virtual images? Can these images be obtained on a screen? Give reasons in support of your answer.

Give three points of differences between real and virtual images.

What is a mirror? Mention the different types of mirrors commonly used.

Define the following terms in connection with reflection of light:Incident ray, reflected ray, point of incidence, normal, angle of incidence and angle of reflection.

State the laws of reflection of light.

Are the laws of reflection applicable to plane surfaces also valid for curved surfaces?

State the important properties of images formed by plane mirrors.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Define the following terms in connection with reflection of light:
Incident ray, reflected ray, point of incidence, normal, angle of incidence and angle of reflection.