C
CraftExam
high importancemedium8 min

Lens Formula

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

Practice This Concept

Learn the concept

Student-friendly explanation

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.

How to write this in exams

  1. 1

    Start with the exact idea

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

  2. 2

    Then show how to use it

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

  3. 3

    Add one concrete example

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

  4. 4

    Avoid this incomplete answer

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

Definition

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

Example

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

Rule to remember

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

Memory hook

Lens formula is mirror formula with its own sign pattern.

Examples and method

Worked example

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

Method to apply

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

Diagram support

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

How CBSE asks it

Problems usually ask you to find image distance, focal length, or the sign of image position from given data.

Avoid common mistakes

Common confusion

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

Common wrong answer

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

Exam tip

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

Quick check

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

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.

Answer writing and exam use

1-mark answer

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

2-mark answer

The lens formula relates object distance, image distance, and focal length for a thin lens. Lens formula: 1/f = 1/v - 1/u, with distances measured from the optical centre using the Cartesian sign convention. For a convex lens with f = 15 cm and u = -30 cm, the image distance is 30 cm.

3-mark answer

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. Lens formula: 1/f = 1/v - 1/u, with distances measured from the optical centre using the Cartesian sign convention. For a convex lens with f = +15 cm and u = -30 cm, 1/15 = 1/v - 1/(-30). Solving gives 1/v = 1/30, so v = +30 cm. Problems usually ask you to find image distance, focal length, or the sign of image position from given data. Using the mirror formula instead of the lens formula, or keeping the wrong sign for object distance.
MCQ Quiz

Practice this concept with focused MCQs

Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.

10 MCQs5 MinutesInstant Results
Practice This Concept

Help improve this page

Found something confusing, incorrect, or missing?

Practice This Concept