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Mirror Formula

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

In one line: Formula is short; sign convention is the real test.

Understand it

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.

Example

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

Formula and rule

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

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

1For a concave mirror, if u = -30 cm and f = -15 cm, then 1/(-15) = 1/v + 1/(-30).
2Solving gives v = -30 cm.

Method you can reuse

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

Sketch it in your answer

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

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

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

Think first, then show answer

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.

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.

Don't mix this up

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

Exam tip

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

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

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

1
Enough for 1 mark
The mirror formula relates object distance, image distance, and focal length for spherical mirrors.
2
Add for 2 marks
Example: A concave mirror with f = -15 cm and u = -30 cm gives v = -30 cm.
3
Add for 3 marks
Using the Cartesian sign convention, 1/f = 1/v + 1/u.

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