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medium importancemedium difficulty5 min

Lens Formula

The lens formula relates object distance, image distance, and focal length for a thin lens.

In one line: Lens formula is mirror formula with its own sign pattern.

Practice This Concept

Understand it

For class 10, use 1/f = 1/v - 1/u with Cartesian sign convention. It works for both convex and concave lenses if signs are applied correctly. The formula helps predict whether the image will be real or virtual and how far it will form.

Example

For a convex lens with f = 15 cm and u = -30 cm, the image distance is 30 cm.

Formula and rule

Lens formula: 1/f = 1/v - 1/u, with distances measured from the optical centre using the Cartesian sign convention.

See it worked out

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

Worked example

  1. 1For a convex lens with f = +15 cm and u = -30 cm, 1/15 = 1/v - 1/(-30).
  2. 2Solving gives 1/v = 1/30, so v = +30 cm.

Method you can reuse

  1. 1Write the formula.
  2. 2Put correct signs for u, v, and f.
  3. 3Substitute.
  4. 4Solve and read the sign of v.

Sketch it in your answer

Draw the principal axis, optical centre, focal points on both sides, object, and image, then label u, v, and f.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

A convex lens has focal length 15 cm and an object at 30 cm in front of it. Where will the image form?

Think first, then show answer
The image will form 30 cm on the other side of the lens because substituting u = -30 cm and f = +15 cm in the lens formula gives v = +30 cm.

Common wrong answer

Using the mirror formula instead of the lens formula, or keeping the wrong sign for object distance.

Don't mix this up

Students often use 1/f = 1/u + 1/v or forget that object distance is negative in front of the lens.

Exam tip

A real object is usually placed on the left side, so u is negative in the Cartesian sign system.

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 the sign of image position from given data.
  1. 1

    Enough for 1 mark

    The lens formula relates object distance, image distance, and focal length for a thin lens.

  2. 2

    Add for 2 marks

    Example: For a convex lens with f = 15 cm and u = -30 cm, the image distance is 30 cm.

  3. 3

    Add for 3 marks

    It works for both convex and concave lenses if signs are applied correctly.

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