Formula
Lens maker's formula
1/f = (n - 1)(1/R₁ - 1/R₂). Determines focal length from material refractive index and surface curvatures.
-- NCERT Class 12 Physics, Ch. 9, p. 232Lens Makers Formula
8 MCQs1 revision card9-step worked example
Source: NCERT OpticsPYQ coverage: NEET 2022Official key: NTA-verifiedLast updated: 27 Sep 2026
Lens Makers Formula, explained for NEET
The lens maker's formula answers a question the thin lens formula never touches: where does f come from in the first place? A lens has no focal length of its own — it inherits one from the glass it is cut from and the two spheres its surfaces are ground to.
NCERT Class 12 Physics, Chapter 9, page 232 states it as
1/f = (n − 1)(1/R₁ − 1/R₂)
Three things in that line are worth slowing down for.
R₁ and R₂ belong to specific surfaces, not to "the front" and "the back" by shape. R₁ is the radius of the surface the light meets first, R₂ the second. Swap them and the sign of 1/f flips. Each radius is signed by the same Cartesian rule used everywhere in this chapter: measured from the surface's pole, positive when the centre of curvature lies on the outgoing side of the light. So a biconvex lens has R₁ positive and R₂ negative, and the bracket becomes a sum of two positive terms — that minus sign in the formula is not doing subtraction of magnitudes.
The (n − 1) factor is a relative index, and the "− 1" is the surrounding medium. The formula as printed assumes the lens sits in air. Immerse the same glass lens in water and n becomes n_lens/n_medium, so (n − 1) shrinks and f grows. A lens of the same index as its surroundings has infinite focal length: optically, it disappears. This is why the conditions of use list "lens in air" alongside "thin lens" — the second one matters too, since the formula treats both refractions as happening at a single plane.
What the formula does not contain is the object. No u, no v. Focal length is a property of the lens alone. Whether the image lands 20 cm away or 2 m away is then the thin lens formula's job, on its own page.
Watch-out: writing 1/f and reading it as f. The left side is a reciprocal, in m⁻¹.
Can you answer these Lens Makers Formula 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 lens maker's formula expresses the focal length of a thin lens in terms of
Show answer and why every option is right or wrong
Answer: D. D is correct. NCERT Class 12 Physics, Chapter 9, page 232 gives 1/f = (n − 1)(1/R₁ − 1/R₂) — the focal length follows from the material's refractive index and the two surface curvatures alone.
Why A is wrong: A is wrong because object and image distances appear in the thin lens formula, which locates an image for a lens whose f is already known. The lens maker's formula contains no u and no v.
Why B is wrong: B is wrong because power is 1/f, so it is the same quantity as focal length restated, not an independent input. Image distance does not enter the formula at all.
Why C is wrong: C is wrong because neither aperture nor centre thickness appears in the formula. The thin-lens condition in fact requires the thickness to be negligible.
MCQ 2Easy RecallPractice
In the lens maker's formula 1/f = (n − 1)(1/R₁ − 1/R₂), the symbol R₁ denotes the radius of curvature of
Show answer and why every option is right or wrong
Answer: B. B is correct. The subscripts are ordered by the path of the light: R₁ is the first refracting surface encountered, R₂ the second, per NCERT Class 12 Physics, Chapter 9, page 232.
Why A is wrong: A is wrong because the labels are fixed by the order of refraction, not by comparing magnitudes. The more strongly curved surface may be either the first or the second.
Why C is wrong: C is wrong because a lens may have two convex surfaces, or a convex and a concave surface; shape does not assign the subscript. Reversing the direction of incidence reassigns R₁ and R₂.
Why D is wrong: D is wrong because the image position is an outcome of using the formula, not an input that labels the surfaces.
MCQ 3Easy RecallPractice
The lens maker's formula in the form 1/f = (n − 1)(1/R₁ − 1/R₂) is valid under the assumption that the lens is
Show answer and why every option is right or wrong
Answer: C. C is correct. The stated conditions of use are a thin lens, both surfaces signed by the convention, and the lens in air — as given with the formula in NCERT Class 12 Physics, Chapter 9, page 232.
Why A is wrong: A is wrong because the thin-lens assumption is exactly what lets both refractions be treated as occurring at one plane. A thick lens needs a modified treatment.
Why B is wrong: B is wrong because the formula covers paraxial rays generally, not only rays travelling along the axis itself. A ray exactly on the axis would form no off-axis image.
Why D is wrong: D is wrong because the formula applies to diverging lenses too; there it returns a negative f rather than failing.
MCQ 4Direct ApplicationPractice
A thin double-convex lens is made of glass of refractive index 1.50 and each of its surfaces has a radius of curvature of magnitude 2.00 × 10⁻¹ m. With the lens in air, its focal length is
Show answer and why every option is right or wrong
Answer: A. A is correct. For a double-convex lens R₁ = +2.00 × 10⁻¹ m and R₂ = −2.00 × 10⁻¹ m, so 1/f = (1.50 − 1)(1/0.200 − 1/(−0.200)) = 0.50 × 10.0 m⁻¹ = 5.00 m⁻¹, giving f = 2.00 × 10⁻¹ m. The formula is NCERT Class 12 Physics, Chapter 9, page 232.
Why B is wrong: B is wrong because it results from omitting the (n − 1) factor and using 1/f = 1/R₁ − 1/R₂ = 10.0 m⁻¹. The refractive index cannot be dropped; a lens of n = 1 has no focal length at all.
Why C is wrong: C is wrong because it comes from taking R₂ as positive, so that the bracket becomes 1/0.200 − 1/0.200 = 0 — or, in the version that yields this number, from using only one surface: (n − 1)/R = 2.5 m⁻¹. A double-convex lens refracts at both surfaces, and both contribute.
Why D is wrong: D is wrong because it is the reciprocal misread: the calculation gives 1/f = 5.00 m⁻¹, and reporting 5.00 × 10⁻² m treats that number as though it were already a length in centimetres.
MCQ 5Direct ApplicationPractice
A thin plano-convex lens has its curved surface facing the incoming light, with radius of curvature of magnitude 1.50 × 10⁻¹ m; the other surface is flat. The glass has refractive index 1.60 and the lens is in air. The focal length is
Show answer and why every option is right or wrong
Answer: A. A is correct. A plane surface has infinite radius, so 1/R₂ = 0 and the second term vanishes: 1/f = (1.60 − 1)(1/0.150) = 0.60 × 6.67 m⁻¹ = 4.00 m⁻¹, so f = 2.50 × 10⁻¹ m. Applies NCERT Class 12 Physics, Chapter 9, page 232.
Why B is wrong: B is wrong because it uses n rather than (n − 1): 1.60 × 6.67 = 10.7 m⁻¹, which inverts to 9.38 × 10⁻² m.
Why C is wrong: C is wrong because it comes from setting the flat surface's radius to the same 1.50 × 10⁻¹ m as the curved one — treating the lens as double-convex and doubling the bracket to 13.3 m⁻¹. A plane surface has R → ∞, so its reciprocal is zero, not another finite term.
Why D is wrong: D is wrong because it multiplies the radius by n, 0.150 × 1.60 = 0.240 m, instead of dividing by (n − 1); for this geometry f = R/(n − 1) = 0.150/0.60.
MCQ 6Direct ApplicationPractice
Two thin lenses have identical surface curvatures, but one is made of glass of refractive index 1.50 and the other of a plastic of refractive index 1.70. Comparing the two lenses in air, the lens of higher refractive index has
Show answer and why every option is right or wrong
Answer: B. B is correct. With the curvature bracket fixed, 1/f is proportional to (n − 1): raising n from 1.50 to 1.70 raises (n − 1) from 0.50 to 0.70, so 1/f grows and f shrinks. From NCERT Class 12 Physics, Chapter 9, page 232.
Why A is wrong: A is wrong because it reads the proportionality off 1/f as though it applied to f. Refractive index is proportional to 1/f, so f varies inversely with (n − 1).
Why C is wrong: C is wrong because the sign of f is set by the bracket (1/R₁ − 1/R₂), which is unchanged. Both n values exceed 1, so (n − 1) stays positive and cannot flip the sign.
Why D is wrong: D is wrong because curvature is only one of the two inputs; the material index is the other and it differs here.
MCQ 7Concept TrapPractice
A thin converging glass lens of refractive index 1.50 is taken from air and fully immersed in water of refractive index 1.33. Its focal length in water, compared with its focal length in air, is
Show answer and why every option is right or wrong
Answer: D. D is correct. The formula is stated for a lens in air; in a medium the index becomes relative, n_lens/n_medium = 1.50/1.33 ≈ 1.13, so the factor falls from 0.50 to about 0.13 and f grows by roughly a factor of four. The "lens in air" condition attached to the formula in NCERT Class 12 Physics, Chapter 9, page 232 is what this question probes.
Why A is wrong: A is wrong because focal length is a property of the lens and its surroundings. Refraction at each surface depends on the index contrast across it, and immersion changes that contrast.
Why B is wrong: B is wrong because the sign flips only if the surrounding medium is optically denser than the lens, making n_lens/n_medium less than 1. Here 1.50 > 1.33, so the lens still converges — more weakly.
Why C is wrong: C is wrong because it inverts the reasoning: water reduces the contrast between lens and surroundings, so each surface bends the ray less, not more. Less bending means a longer focal length.
MCQ 8CalculationPractice
A thin lens in air has one convex surface of radius of curvature 1.00 × 10⁻¹ m facing the incident light and one concave surface of radius of curvature 2.00 × 10⁻¹ m behind it, both centres of curvature lying on the same side of the lens. The glass has refractive index 1.50. The focal length of this lens is
Show answer and why every option is right or wrong
Answer: C. C is correct. This is a meniscus lens: light meets the convex surface first, so R₁ = +1.00 × 10⁻¹ m, and the second surface curves the same way, so R₂ = +2.00 × 10⁻¹ m. Then 1/f = (0.50)(1/0.100 − 1/0.200) = 0.50 × 5.00 m⁻¹ = 2.50 m⁻¹, so f = 4.00 × 10⁻¹ m, converging. Follows the signed application of NCERT Class 12 Physics, Chapter 9, page 232.
Why A is wrong: A is wrong because it comes from ordering the radii the wrong way round — taking R₁ = 2.00 × 10⁻¹ m and R₂ = 1.00 × 10⁻¹ m, which makes the bracket −5.00 m⁻¹. The subscripts follow the light, and the convex surface is struck first.
Why B is wrong: B is wrong because it results from adding the two reciprocals rather than subtracting them: (0.50)(10.0 + 5.00) = 7.50 m⁻¹. The sign convention has already made R₂ positive here, so the formula's minus sign performs a genuine subtraction in this case.
Why D is wrong: D is wrong because 6.67 × 10⁻² m is 1/15.0: it takes R₂ as negative and also drops the (n − 1) factor, giving 1/f = 10.0 + 5.00 = 15.0 m⁻¹. With both centres on the same side, R₁ = +0.100 m and R₂ = +0.200 m, so 1/f = 0.50(10.0 − 5.00) = 2.50 m⁻¹ and f = 0.400 m.
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Lens Makers Formula: quick recall before you leave
How do you solve a Lens Makers Formula question? A worked example
- 1
Given
A thin double-convex lens is made of glass of refractive index n_g = 1.50 (exact, as specified). Both surfaces have radius of curvature of magnitude 2.00 × 10⁻¹ m. The lens is first in air (n = 1.00, exact by definition of the reference medium), then fully immersed in water of refractive index n_w = 1.33.
- 2
Required
The focal length in air, and the focal length in water.
- 3
Concept
Focal length is not intrinsic to the lens: it depends on the index of the lens relative to the medium surrounding it. The printed formula's (n − 1) is the air case of the general factor (n_lens/n_medium − 1).
- 4
Formula
1/f = (n − 1)(1/R₁ − 1/R₂), with n replaced by n_lens/n_medium when the lens is not in air.
- 5
Substitution
Double-convex, light entering from the left: R₁ = +2.00 × 10⁻¹ m, R₂ = −2.00 × 10⁻¹ m.
Bracket: 1/R₁ − 1/R₂ = 1/(0.200) − 1/(−0.200) = 5.00 + 5.00 = 10.0 m⁻¹.
In air: 1/f_air = (1.50 − 1.00)(10.0) m⁻¹.
In water: relative index = 1.50/1.33 = 1.128, so 1/f_water = (1.128 − 1.00)(10.0) m⁻¹. - 6
Calculation
1/f_air = 0.500 × 10.0 = 5.00 m⁻¹.
1/f_water = 0.128 × 10.0 = 1.28 m⁻¹.
The "1" subtracted inside each bracket is the exact refractive index of the reference medium, and the 10.0 m⁻¹ bracket carries three significant figures from the given radii. Neither the "1" nor the signs contribute to the significant-figure count; the result is limited by the given data at three figures. - 7
Final answer
f_air = 1/5.00 m⁻¹ = 2.00 × 10⁻¹ m.
f_water = 1/1.28 m⁻¹ = 7.81 × 10⁻¹ m.
Immersion lengthens the focal length by a factor of about 3.9. The lens still converges, because the glass remains optically denser than the water. - 8
Common trap
Reporting 5.00 × 10⁻¹ m or 1.28 m as the focal length — that is, handing back 1/f with a unit attached. The left-hand side of the lens maker's formula is a reciprocal length in m⁻¹, numerically equal to the power in dioptres. Invert it as the last step, every time. The second trap in this problem is leaving (n − 1) at 0.50 after immersion: the subtracted 1 is the medium, and the medium changed.
- 9
Similar NEET-style question
A thin equiconvex lens of refractive index 1.50 has a focal length of 1.50 × 10⁻¹ m in air. It is immersed in a liquid of refractive index 1.25. Its focal length in the liquid is closest to (a) 1.50 × 10⁻¹ m (b) 3.00 × 10⁻¹ m (c) 4.50 × 10⁻¹ m (d) 7.50 × 10⁻¹ m. Method: the bracket is unchanged, so f scales as 1/(n_rel − 1); (0.50)/(1.50/1.25 − 1) = 0.50/0.20 = 2.5, giving 3.75 × 10⁻¹ m — pick the nearest listed value and check your scaling against it.
What to remember before solving Lens Makers Formula questions
Which Lens Makers Formula formulas do you need for NEET?
1 formula — click to collapse
Lens maker's formula
Focal length from refractive index and surface curvatures.
| Symbol | Quantity | SI Unit |
|---|---|---|
| f | focal length | m |
| n | refractive index | - |
| R1, R2 | radii of curvature | m |
Valid when
- Thin lens
- Both surfaces specified with sign convention
- Lens in air
More in Optics: 9 exam traps and mistakes · 10 formulas · 7 question patterns from its other lessons.
Lens Makers Formula questions from past NEET papers
1 question from NEET 2022. Answers verified against NTA official keys. — click to collapse
NEET 2022
1Infinity
2+2 D
3+20 D
4+5 D
NTA Answer: Option 4(final)
Sources
NCERT refs: Class 12 Physics Chapter 9, p.232
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.
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