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Lens formula and magnification: Class 10 practice

For a thin lens, 1/v − 1/u = 1/f with the Cartesian sign convention (distances measured from the optical centre; object distance u is negative). Read the method, follow the three worked examples, then try the six questions.

What you should know first

  • Fractions with negatives

The idea behind lens formula and magnification

For a thin lens, 1/v − 1/u = 1/f with the Cartesian sign convention (distances measured from the optical centre; object distance u is negative). Magnification m = v/u.

Step-by-step method

  1. Apply signs: u negative, f positive for a convex lens, negative for concave.
  2. 1/v = 1/f + 1/u.
  3. m = v/u; negative m means a real, inverted image.
  4. Power P = 1/f (f in metres), in dioptres.

Worked example 1 (Basic)

An object is 40 cm in front of a convex lens of focal length 24 cm. Find the image position and magnification.

  1. u = -40 cm, f = 24 cm
  2. 1/v = 1/24 + 1/(-40) = 1/60
  3. v = 60 cm
  4. m = v/u = -3/2
  5. Real, inverted image on the other side
  6. Answer: v = 60 cm, m = -3/2

Worked example 2 (Standard)

An object is 20 cm in front of a convex lens of focal length 15 cm. Find the image position and magnification.

  1. u = -20 cm, f = 15 cm
  2. 1/v = 1/15 + 1/(-20) = 1/60
  3. v = 60 cm
  4. m = v/u = -3
  5. Real, inverted image on the other side
  6. Answer: v = 60 cm, m = -3

Worked example 3 (Challenge)

An object is 15 cm in front of a concave lens of focal length 10 cm. Find the image position and magnification.

  1. u = -15 cm, f = -10 cm
  2. 1/v = 1/-10 + 1/(-15) = -1/6
  3. v = -6 cm
  4. m = v/u = 2/5
  5. Virtual, erect image on the same side
  6. Answer: v = -6 cm, m = 2/5

Common mistakes and misconceptions

  • Using the mirror formula (1/v + 1/u)
  • Dropping the minus sign on u

Practice questions

  1. (Basic) An object is 60 cm in front of a convex lens of focal length 20 cm. Find the image position and magnification.
  2. (Basic) An object is 30 cm in front of a convex lens of focal length 20 cm. Find the image position and magnification.
  3. (Standard) An object is 15 cm in front of a convex lens of focal length 10 cm. Find the image position and magnification.
  4. (Standard) An object is 36 cm in front of a convex lens of focal length 12 cm. Find the image position and magnification.
  5. (Challenge) An object is 12 cm in front of a concave lens of focal length 12 cm. Find the image position and magnification.
  6. (Challenge) An object is 60 cm in front of a concave lens of focal length 20 cm. Find the image position and magnification.

Answer key with full working

  • Q1: u = -60 cm, f = 20 cm → 1/v = 1/20 + 1/(-60) = 1/30 → v = 30 cm → m = v/u = -1/2 → Real, inverted image on the other side → Answer: v = 30 cm, m = -1/2
  • Q2: u = -30 cm, f = 20 cm → 1/v = 1/20 + 1/(-30) = 1/60 → v = 60 cm → m = v/u = -2 → Real, inverted image on the other side → Answer: v = 60 cm, m = -2
  • Q3: u = -15 cm, f = 10 cm → 1/v = 1/10 + 1/(-15) = 1/30 → v = 30 cm → m = v/u = -2 → Real, inverted image on the other side → Answer: v = 30 cm, m = -2
  • Q4: u = -36 cm, f = 12 cm → 1/v = 1/12 + 1/(-36) = 1/18 → v = 18 cm → m = v/u = -1/2 → Real, inverted image on the other side → Answer: v = 18 cm, m = -1/2
  • Q5: u = -12 cm, f = -12 cm → 1/v = 1/-12 + 1/(-12) = -1/6 → v = -6 cm → m = v/u = 1/2 → Virtual, erect image on the same side → Answer: v = -6 cm, m = 1/2
  • Q6: u = -60 cm, f = -20 cm → 1/v = 1/-20 + 1/(-60) = -1/15 → v = -15 cm → m = v/u = 1/4 → Virtual, erect image on the same side → Answer: v = -15 cm, m = 1/4

Syllabus note

This skill is listed under "Light – Reflection and Refraction" for Class 10 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.

Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.

Related practice and notes

Frequently asked questions

Which chapter is lens formula and magnification in?

"Light – Reflection and Refraction", Class 10 Physics (NCERT/CBSE). Other boards may place it differently.

How were the answers checked?

Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.

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