A relationship between the distance of the object from the pole (u), distance of the image from the pole (v) and the focal length (f) of the mirror is called the mirror formula.

In a spherical mirror ,the distance of the object from its pole is called the object distance.

The distance of the image from the pole of the mirror is called the image distance.

The distance of the principal focus from the pole is called focal length.

Relation Between u, v, f:

For any spherical mirror of small aperture, and for any position of the object, the three quantities u, v and f satisfy the simple algebraic relation given below.

Mirror Equation

$large frac{1}{v}+frac{1}{u}=frac{1}{f}$

Remember that u, v, f can be positive or negative depending on the geometry of the situation.

1. In the mirror formula the values of u,v and f are to be used according to their Cartesian sign convention .

2. The mirror formula is valid in all situation for all spherical mirrors and for all positions of the object .

Illustration: An object is placed at a distance of 30 cm from a concave mirror of focal length 20 cm. Where will the image be formed?

Solution:It is given that we have a concave mirror, so the focal length will be negative.

The distance of the object is always negative.

We have, u = -30 cm and f = -20 cm.

Also according to the mirror formula,

$large frac{1}{v}+frac{1}{u}=frac{1}{f}$

$large Rightarrow ;;;frac{1}{v}=frac{1}{f}-frac{1}{u}$

Substituting the values in the formula we get,

$large Rightarrow ;;;frac{1}{v}=frac{1}{-20;cm}-frac{1}{-30;cm}$

$large Rightarrow ;;;frac{1}{v}=frac{1}{-20;cm}+frac{1}{30;cm}=frac{-3+2}{60 cm}=-frac{1}{60cm}$

or v = -60 cm.

So, the distance of the image will be 60 cm from the mirror. Since v has a negative sign, the image is formed to the left of the mirror, i.e., in front of it.

Sample Questions

(More Questions for each concept available in Login)

Question : 1

Which of the following are correct ? (a) A relationship between the distance of the object from the pole , distance of the image from the pole and the focal length of the mirror is called the mirror formula. (b) In the mirror formula the values of u,v and f are to be used according to their Cartesian sign convention . (c) The mirror formula is valid in all situation for all spherical mirrors and for all positions of the object .
A. Only (a) and (b) is correct .	B. Only (b) and (c) is correct .	C. Only (a) and (c) is correct .	D. All of these .
Right Option : D
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Question : 2

A relationship between the distance of the object from the pole (u), distance of the image from the pole (v) and the focal length (f) of the mirror is called the ____________________ .
A. Lens formula	B. Mirror formula	C. Both (a) and (b) is correct .	D. None of these .
Right Option : B
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Question : 3

Which of the following are correct ? (a) In a spherical mirror, the distance of the object from its pole is called the object distance . (b) The distance of the principal focus from the pole is called focal length . (c) In case of spherical mirror the relation between quantities u, v, f is called lens formula .
A. Only (a) and (b) is correct .	B. Only (b) and (c) is correct .	C. Only (a) and (c) is correct.	D. All of these .
Right Option : A
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