Lens maker's formula: Class 12 practice
1/f = (n − 1)(1/R₁ − 1/R₂), with radii signed by the Cartesian convention (for a biconvex lens R₁ > 0, R₂ < 0). Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Fractions
- Sign convention
The idea behind lens maker's formula
1/f = (n − 1)(1/R₁ − 1/R₂), with radii signed by the Cartesian convention (for a biconvex lens R₁ > 0, R₂ < 0). A lens in a liquid has (n_lens/n_liquid − 1) instead of (n − 1).
Step-by-step method
- Assign signs to R₁ and R₂.
- Substitute into the formula.
- In a liquid, replace n by n_lens/n_liquid.
Worked example 1 (Basic)
A biconvex lens has both radii 15 cm and n = 1.5. Find its focal length.
- 1/f = (1.5 − 1)(1/15 − 1/(−15))
- f = 15 cm
- Answer: 15 cm
Worked example 2 (Standard)
A plano-convex lens (n = 1.5) has curved surface radius 39 cm. Find f.
- 1/f = (1.5 − 1)(1/39 − 0)
- f = 78 cm
- Answer: 78 cm
Worked example 3 (Challenge)
The biconvex lens above (n = 1.6, R = 11 cm) is put in water (n = 1.33). Find its new focal length.
- 1/f = (1.6/1.33 − 1)(2/11)
- f = 27.09 cm
- Answer: 27.09 cm
Common mistakes and misconceptions
- Taking both radii as positive for a biconvex lens
- Using n − 1 in a liquid
Practice questions
- (Basic) A biconvex lens has both radii 35 cm and n = 1.5. Find its focal length.
- (Basic) A biconvex lens has both radii 14 cm and n = 1.6. Find its focal length.
- (Standard) A plano-convex lens (n = 1.5) has curved surface radius 28 cm. Find f.
- (Standard) A plano-convex lens (n = 1.6) has curved surface radius 32 cm. Find f.
- (Challenge) The biconvex lens above (n = 1.5, R = 22 cm) is put in water (n = 1.33). Find its new focal length.
- (Challenge) The biconvex lens above (n = 1.5, R = 28 cm) is put in water (n = 1.33). Find its new focal length.
Answer key with full working
- Q1: 1/f = (1.5 − 1)(1/35 − 1/(−35)) → f = 35 cm → Answer: 35 cm
- Q2: 1/f = (1.6 − 1)(1/14 − 1/(−14)) → f = 11.67 cm → Answer: 11.67 cm
- Q3: 1/f = (1.5 − 1)(1/28 − 0) → f = 56 cm → Answer: 56 cm
- Q4: 1/f = (1.6 − 1)(1/32 − 0) → f = 53.33 cm → Answer: 53.33 cm
- Q5: 1/f = (1.5/1.33 − 1)(2/22) → f = 86.06 cm → Answer: 86.06 cm
- Q6: 1/f = (1.5/1.33 − 1)(2/28) → f = 109.53 cm → Answer: 109.53 cm
Syllabus note
This skill is listed under "Ray Optics" for Class 12 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 maker's formula in?
"Ray Optics", Class 12 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.