Power of a lens and lens combinations: Class 10 practice
Power P = 1/f with f in metres; unit dioptre (D). Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Fractions
- Sign convention
The idea behind power of a lens and lens combinations
Power P = 1/f with f in metres; unit dioptre (D). Convex lenses have positive power, concave negative. Lenses in contact add their powers: P = P₁ + P₂.
Step-by-step method
- Convert f to metres.
- P = 1/f (with sign).
- For lenses in contact add the powers, then f = 1/P.
Worked example 1 (Basic)
Find the power of a lens of focal length -50 cm.
- f = -0.5 m
- P = 1/f = -2 D (concave)
- Answer: -2 D
Worked example 2 (Standard)
Lenses of +5 D and -1 D are placed in contact. Find the combined power and focal length.
- P = 5 + (-1) = 4 D
- f = 1/4 m = 25 cm
- Answer: 4 D, 25 cm
Worked example 3 (Challenge)
A doctor prescribes 2 D. What lens and focal length is this?
- f = 1/P = 0.5 m = 50 cm
- Convex (converging)
- Answer: Convex, f = 50 cm
Common mistakes and misconceptions
- Using f in cm
- Adding focal lengths
Practice questions
- (Basic) Find the power of a lens of focal length -25 cm.
- (Basic) Find the power of a lens of focal length -100 cm.
- (Standard) Lenses of +4 D and -1 D are placed in contact. Find the combined power and focal length.
- (Standard) Lenses of +2 D and -1 D are placed in contact. Find the combined power and focal length.
- (Challenge) A doctor prescribes 5 D. What lens and focal length is this?
- (Challenge) A doctor prescribes 4 D. What lens and focal length is this?
Answer key with full working
- Q1: f = -0.25 m → P = 1/f = -4 D (concave) → Answer: -4 D
- Q2: f = -1 m → P = 1/f = -1 D (concave) → Answer: -1 D
- Q3: P = 4 + (-1) = 3 D → f = 1/3 m = 33.33 cm → Answer: 3 D, 33.33 cm
- Q4: P = 2 + (-1) = 1 D → f = 1/1 m = 100 cm → Answer: 1 D, 100 cm
- Q5: f = 1/P = 0.2 m = 20 cm → Convex (converging) → Answer: Convex, f = 20 cm
- Q6: f = 1/P = 0.25 m = 25 cm → Convex (converging) → Answer: Convex, f = 25 cm
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
- Light Reflection and Refraction chapter notes (Class 10)
- Mirror formula and magnification
- Refractive index and speed of light
- Snell's law
- Ohm's law and resistors in series and parallel
- Electric power and energy consumption
- Lens formula and magnification
- Resistivity and resistance of a wire
- All Class 10 practice
Frequently asked questions
Which chapter is power of a lens and lens combinations 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.