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Mirror Formula

The mirror formula relates object distance, image distance, and focal length for spherical mirrors.

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Student-friendly explanation

Using the Cartesian sign convention, 1/f = 1/v + 1/u. This formula helps calculate where the image forms and whether it is real or virtual. Correct signs are essential because the same mirror can give very different images depending on object position.

How to write this in exams

  1. 1

    Start with the exact idea

    The mirror formula relates object distance, image distance, and focal length for spherical mirrors.

  2. 2

    Then show how to use it

    1. Write the formula. 2. Apply the sign convention. 3. Substitute values carefully. 4. Solve for the unknown and interpret the sign.

  3. 3

    Add one concrete example

    A concave mirror with f = -15 cm and u = -30 cm gives v = -30 cm.

  4. 4

    Avoid this incomplete answer

    Using the wrong sign for object distance in front of the mirror. That changes the answer even if the arithmetic is correct.

Definition

The mirror formula relates object distance, image distance, and focal length for spherical mirrors.

Example

A concave mirror with f = -15 cm and u = -30 cm gives v = -30 cm.

Rule to remember

Mirror formula: 1/f = 1/v + 1/u, with distances measured from the pole using Cartesian sign convention.

Memory hook

Formula is short; sign convention is the real test.

Examples and method

Worked example

For a concave mirror, if u = -30 cm and f = -15 cm, then 1/(-15) = 1/v + 1/(-30). Solving gives v = -30 cm.

Method to apply

1. Write the formula. 2. Apply the sign convention. 3. Substitute values carefully. 4. Solve for the unknown and interpret the sign.

Diagram support

Draw the mirror, pole, principal axis, object, image, and mark distances u, v, and f with correct signs.

How CBSE asks it

Problems usually ask you to find image distance, focal length, or object position using a numerical setup.

Avoid common mistakes

Common confusion

Students often insert all distances as positive numbers and then get the wrong image position.

Common wrong answer

Using the wrong sign for object distance in front of the mirror. That changes the answer even if the arithmetic is correct.

Exam tip

Write the sign convention before starting the calculation; it saves many mistakes.

Quick check

A concave mirror has f = -10 cm and an object at u = -20 cm. What is the image distance?

The image distance is -20 cm. Using 1/f = 1/v + 1/u gives 1/(-10) = 1/v + 1/(-20), so v also comes out as -20 cm.

Answer writing and exam use

1-mark answer

The mirror formula relates object distance, image distance, and focal length for spherical mirrors.

2-mark answer

The mirror formula relates object distance, image distance, and focal length for spherical mirrors. Mirror formula: 1/f = 1/v + 1/u, with distances measured from the pole using Cartesian sign convention. A concave mirror with f = -15 cm and u = -30 cm gives v = -30 cm.

3-mark answer

Using the Cartesian sign convention, 1/f = 1/v + 1/u. This formula helps calculate where the image forms and whether it is real or virtual. Correct signs are essential because the same mirror can give very different images depending on object position. Mirror formula: 1/f = 1/v + 1/u, with distances measured from the pole using Cartesian sign convention. For a concave mirror, if u = -30 cm and f = -15 cm, then 1/(-15) = 1/v + 1/(-30). Solving gives v = -30 cm. Problems usually ask you to find image distance, focal length, or object position using a numerical setup. Using the wrong sign for object distance in front of the mirror. That changes the answer even if the arithmetic is correct.
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