Formula
Thin lens formula
1/v - 1/u = 1/f. Same sign convention as for mirrors. Power P = 1/f (in dioptres if f in metres).
-- NCERT Class 12 Physics, Ch. 9, p. 234Power of Lens
8 MCQs1 revision card9-step worked example
Source: NCERT OpticsOfficial key: NTA-verifiedLast updated: 25 Sep 2026
Power of Lens, explained for NEET
The high-frequency trap here is a unit slip, not a physics error. Power is defined as P = 1/f with f in metres. Hand a student f = 20 cm and the reflex answer is 1/20 = 0.05 D. The correct value is 1/0.20 = 5.0 D — a factor of 100 out, and the wrong number is always sitting in the options.
NCERT Class 12 Physics Chapter 9, page 234, defines the power of a lens as the degree of convergence or divergence it produces, measured as the reciprocal of the focal length in metres. The unit is the dioptre (D): 1 D = 1 m⁻¹. A lens of focal length 1 m has a power of 1 D.
Two consequences follow directly from the reciprocal.
Sign carries over. A converging (convex) lens has positive f, so positive P. A diverging (concave) lens has negative f, so negative P. The sign of the power is the sign of the focal length — nothing new to memorise.
The relationship is inverse, not proportional. A short focal length means a strong lens. Halving f doubles P. Aspirants who reason "bigger focal length, bigger power" get every comparison question backwards.
Watch the direction of conversion too. Going from f to P you divide; going from P back to f you divide again — f = 1/P. A spectacle prescription of −2.5 D corresponds to a diverging lens of focal length 1/(−2.5) = −0.40 m, i.e. 40 cm. Students who multiply instead of dividing land on 2.5 m.
Combination arithmetic (powers adding in contact) is handled in the lenses-in-contact lesson. Here, fix the single-lens definition: metres, reciprocal, sign preserved.
Can you answer these Power of Lens MCQs?
Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.
MCQ 1Easy RecallPractice
The SI unit of power of a lens is the
Show answer and why every option is right or wrong
Answer: C. C is correct. NCERT Class 12 Physics Chapter 9, page 234, gives the dioptre (D) as the unit of lens power, equal to 1 m⁻¹.
Why A is wrong: A is wrong because the watt is the unit of mechanical or radiant power; optical power of a lens is a reciprocal length, unrelated to energy per unit time.
Why B is wrong: B is wrong because the metre is the unit of focal length, not of its reciprocal.
Why D is wrong: D is wrong because the radian measures plane angle; lens power is a reciprocal length.
MCQ 2Easy RecallPractice
The power of a lens of focal length f is defined as
Show answer and why every option is right or wrong
Answer: D. D is correct. NCERT Class 12 Physics Chapter 9, page 234, defines power as the reciprocal of focal length expressed in metres, giving the value in dioptres.
Why A is wrong: A is wrong because power is the reciprocal of focal length, not the focal length itself — a short-focus lens is a strong lens.
Why B is wrong: B is wrong because no square appears in the definition; power has dimensions of inverse length.
Why C is wrong: C is wrong because using centimetres gives a number 100 times too small; the definition fixes the unit of f as the metre (trap: centimetre focal length fed straight into 1/f).
MCQ 3Easy RecallPractice
A lens of power 1.00 D has a focal length in air of
Show answer and why every option is right or wrong
Answer: A. A is correct. Since P = 1/f with f in metres, a power of 1.00 D corresponds to f = 1/1.00 = 1.00 m. This is the reference value from which the dioptre is defined, NCERT Class 12 Physics Chapter 9, page 234.
Why B is wrong: B is wrong because 1.00 × 10⁻¹ m gives P = 10.0 D, not 1.00 D.
Why C is wrong: C is wrong because 1.00 × 10⁻² m (1 cm) would give a power of 100 D — this treats the focal length as though centimetres were the defining unit.
Why D is wrong: D is wrong because 1.00 × 10² m gives P = 1.00 × 10⁻² D; the reciprocal has been applied in the wrong direction.
MCQ 4Direct ApplicationPractice
A thin converging lens has a focal length of 25.0 cm in air. Its power is
Show answer and why every option is right or wrong
Answer: C. C is correct. Converting first, f = 25.0 cm = 0.250 m, so P = 1/0.250 = +4.00 D, positive because the lens converges. NCERT Class 12 Physics Chapter 9, page 234.
Why A is wrong: A is wrong because it comes from 1/25.0 with the focal length left in centimetres — the classic factor-of-100 slip. The definition requires f in metres.
Why B is wrong: B is wrong because 0.250 is the focal length in metres, reported without taking the reciprocal at all.
Why D is wrong: D is wrong because it reports the focal-length number itself as the power, ignoring the reciprocal relation entirely.
MCQ 5Direct ApplicationPractice
A spectacle lens is marked −2.50 D. Its focal length in air is
Show answer and why every option is right or wrong
Answer: B. B is correct. Inverting the definition, f = 1/P = 1/(−2.50) = −0.400 m. The negative sign is preserved, identifying a diverging lens, as set out in NCERT Class 12 Physics Chapter 9, page 234.
Why A is wrong: A is wrong because it copies the power's numerical value across as a focal length in metres without inverting it.
Why C is wrong: C is wrong because it drops the negative sign. Sign carries through the reciprocal unchanged: a negative power means a negative focal length, i.e. a diverging lens.
Why D is wrong: D is wrong because it multiplies by 10 somewhere in the conversion; 1/2.50 is 0.400, not 4.00.
MCQ 6Direct ApplicationPractice
A thin diverging lens has a focal length of magnitude 50.0 cm. Its power is
Show answer and why every option is right or wrong
Answer: B. B is correct. A diverging lens has f = −50.0 cm = −0.500 m, so P = 1/(−0.500) = −2.00 D. NCERT Class 12 Physics Chapter 9, page 234, notes that the sign of the power follows the sign of the focal length.
Why A is wrong: A is wrong because the magnitude is right but the sign is not: a diverging lens has negative focal length and therefore negative power.
Why C is wrong: C is wrong because it applies 1/f with f left in centimetres and then scales wrongly; the reciprocal of −50.0 cm expressed in metres is −2.00 D, not −50.0 D.
Why D is wrong: D is wrong because −5.00 × 10⁻¹ D is the focal length in metres carrying a minus sign, reported without inverting.
MCQ 7Concept TrapPractice
Two thin converging lenses X and Y are made to the same aperture. Lens X has a focal length of 1.0 × 10⁻¹ m and lens Y has a focal length of 4.0 × 10⁻¹ m. Which statement about their powers is correct?
Show answer and why every option is right or wrong
Answer: A. A is correct. P = 1/f gives P_X = 10 D and P_Y = 2.5 D, a ratio of 4 to 1. The shorter-focus lens is the stronger one — NCERT Class 12 Physics Chapter 9, page 234, describes power as the degree of convergence produced.
Why B is wrong: B is wrong because it inverts the relationship. Power is the reciprocal of focal length, so a longer focal length means a weaker, not a stronger, lens.
Why C is wrong: C is wrong because aperture does not enter the definition of power at all; only the focal length does.
Why D is wrong: D is wrong because it treats power as directly proportional to f, which reverses the reciprocal relation.
MCQ 8CalculationPractice
A thin lens forms a real image of a real object placed 3.00 × 10⁻¹ m from it, the image lying 6.00 × 10⁻¹ m on the far side. The power of this lens is
Show answer and why every option is right or wrong
Answer: C. C is correct. Using the thin lens formula with u = −3.00 × 10⁻¹ m and v = +6.00 × 10⁻¹ m, 1/f = 1/v − 1/u = 1/0.600 + 1/0.300 = 5.00 m⁻¹, so f = 0.200 m and P = 1/f = +5.00 D. Note that 1/f in m⁻¹ is the power in dioptres, so no extra step is needed. NCERT Class 12 Physics Chapter 9, page 234.
Why A is wrong: A is wrong because 0.500 is the ratio of the distances, u/v = 0.300/0.600 — the size of the reciprocal magnification, not a power.
Why B is wrong: B is wrong because it subtracts the reciprocals instead of adding them — a sign slip with u = −0.300 m: 1/0.300 − 1/0.600 = 1.67 D.
Why D is wrong: D is wrong because the magnitude is right but the sign is not: a real object forming a real image on the far side requires a converging lens, so the power is positive.
Free NEET study resources
Get a structured 30-day Mechanics plan and a complete formula booklet — delivered to your inbox instantly.
Power of Lens: quick recall before you leave
How do you solve a Power of Lens question? A worked example
- 1
Given
• Required power: P_req = −4.00 D• Measured focal length magnitude: 25.0 cm• Lens type: diverging
- 2
Required
The power of the ground lens, and whether it equals the specified −4.00 D.
- 3
Concept
Power measures how strongly a lens bends light and is the reciprocal of the focal length expressed in metres. A diverging lens carries a negative focal length, and the reciprocal preserves that sign.
- 4
Formula
P = 1/f, f in metres, P in dioptres. - 5
Substitution
Convert before substituting — this is where the factor-of-100 error enters.
f = −25.0 cm = −0.250 m (negative, because the lens diverges)
P = 1/(−0.250 m) - 6
Calculation
P = −4.00 m⁻¹ = −4.00 D
The conversion factor 100 cm = 1 m is exact by definition, as is the relation 1 D = 1 m⁻¹; neither limits the significant figures. The three significant figures come from the measured 25.0 cm alone. - 7
Final answer
P = −4.00 D. The lens meets the specification.
- 8
Common trap
The failure mode is substituting 25.0 rather than 0.250 and obtaining −4.00 × 10⁻² D, then concluding the lens is far too weak and rejecting a perfectly good lens. The second failure mode is reporting +4.00 D by taking the magnitude of the focal length and losing the diverging sign — that describes a converging lens, the opposite of what was made. Convert to metres first, attach the sign to f before inverting.
- 9
Similar NEET-style question
An optician needs a lens of power +2.50 D. Which focal length should be ground?
(Answer: f = 1/2.50 = +0.400 m = 40.0 cm, converging.)
What to remember before solving Power of Lens questions
Which Power of Lens formulas do you need for NEET?
1 formula — click to collapse
Thin lens formula
Thin lens formula. Power P = 1/f (in dioptres if f in metres).
| Symbol | Quantity | SI Unit |
|---|---|---|
| v | image distance | m |
| u | object distance | m |
| f | focal length | m |
Valid when
- Thin lens
- Paraxial rays
- Sign convention used
Where do students lose marks on Power of Lens?
These are the exact patterns that cause wrong answers in NEET. Each trap includes when it triggers and how to avoid it.
1 item — click to collapse
Category: Negative Marking
Sequential 1/F = 1/f1 + 1/f2 across multiple lenses. Each f sign error or reciprocal-skip propagates. Common with diopter conversions (P = 1/f in metres).
When it triggers
Multi-lens optical system; asks for equivalent focal length or power.
How to avoid
Standard procedure: (1) note signs of each f (concave negative); (2) sum 1/f_i; (3) take reciprocal at end. Skip the final reciprocal and the answer is off by orders of magnitude — always present as distractor.
More in Optics: 8 exam traps and mistakes · 10 formulas · 6 question patterns from its other lessons.
Power of Lens questions from past NEET papers
No question in our NEET 2020–2025 set targets this topic directly.
How does NEET ask about Power of Lens?
1 recurring pattern from past papers — click to collapse
Lenses in contact: 1/F = sum(1/f_i) or P = sum(P_i). Concave is negative.
Multi StepMedium
Common distractors
forgets sign of concave
Treats concave f as positive
Sources
NCERT refs: Class 12 Physics Chapter 9, p.234
Page numbers are the ones printed in the current NCERT textbook (2023 rationalised edition), unless marked pre-2023. The books are free at ncert.nic.in.
Test yourself on this topic with real past-paper questions:
Practice this topic →