Mirror equation: 1/v + 1/u = 1/f. Sign convention: distances along principal axis from pole, positive in direction of incident light. Focal length f = R/2 (R = radius of curvature).
-- NCERT Class 12 Physics, Ch. 9, p. 222Mirror Formula
8 MCQs1 revision card9-step worked example
Source: NCERT OpticsOfficial key: NTA-verifiedLast updated: 27 Sep 2026
Mirror Formula, explained for NEET
The mirror formula punishes one thing above all: sign bookkeeping. 1/v + 1/u = 1/f is trivially memorised, but the corpus records inverted signs of u, v, or f as a recurring optics error — the student computes correctly and still marks the wrong option because a minus sign never made it onto the page.
Fix the convention first, then never revisit it mid-problem. Measure all distances from the pole, along the principal axis, taking the direction of incident light as positive. A real object sits on the incoming-light side, so u is negative. A concave mirror's focus lies on the same side as the object, so f is negative; a convex mirror's focus lies behind it, so f is positive. NCERT Class 12 Physics Chapter 9 sets this out on printed page 222, with the formula itself on page 223.
Note the sign difference from the lens relation: the mirror formula adds the reciprocals (1/v + 1/u), the thin lens formula subtracts them. Two formulas, two shapes — they are covered in separate lessons here, and mixing them up is a distinct error from mis-signing a single mirror problem.
What the formula gives you is v from u and f. The sign of the answer then tells you the physics for free: v negative means the image forms on the object's side, so it is real; v positive means it forms behind the mirror, so it is virtual. Students who solve for |v| and discard the sign lose that information and then guess at real-versus-virtual.
Watch out for the concave mirror with an object inside the focal length. The arithmetic looks identical to every other concave case, but the result flips sign — the image turns virtual. Do not decide real-or-virtual before you compute; let the sign decide.
Can you answer these Mirror 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
For a spherical mirror, the relation connecting object distance u, image distance v and focal length f is
Show answer and why every option is right or wrong
Answer: B. B is correct. The spherical mirror formula is 1/v + 1/u = 1/f, stated in NCERT Class 12 Physics Chapter 9, printed page 223.
Why A is wrong: A is wrong because 1/v − 1/u = 1/f is the thin lens formula, not the mirror formula. The two relations differ in the sign between the reciprocals.
Why C is wrong: C is wrong because it rearranges the relation incorrectly: moving 1/u to the other side requires 1/v = 1/f − 1/u, not 1/f + 1/u.
Why D is wrong: D is wrong because the mirror relation is between reciprocals of the distances, not the distances themselves.
MCQ 2Easy RecallPractice
In the mirror formula, all distances u, v and f are measured from the
Show answer and why every option is right or wrong
Answer: A. A is correct. Under the Cartesian convention set out in NCERT Class 12 Physics Chapter 9, printed page 222, every distance in the mirror formula is measured from the pole, along the principal axis.
Why B is wrong: B is wrong because the focus is itself located by a measurement from the pole — it cannot also be the reference point.
Why C is wrong: C is wrong because the centre of curvature is a located point on the axis, not the origin of measurement; measuring from it would shift every distance by R.
Why D is wrong: D is wrong because the origin must be fixed by the mirror, not by where the object happens to sit; otherwise u would always be zero.
MCQ 3Easy RecallPractice
Under the sign convention used with the mirror formula, the direction taken as positive along the principal axis is the direction
Show answer and why every option is right or wrong
Answer: D. D is correct. The convention described in NCERT Class 12 Physics Chapter 9, printed page 222, takes distances measured in the direction of the incident light as positive.
Why A is wrong: A is wrong because the convention exists precisely so that distances carry signs; using magnitudes only discards the information that distinguishes a real image from a virtual one.
Why B is wrong: B is wrong because it reverses the convention; adopting it would make every sign in a worked solution the opposite of the standard result.
Why C is wrong: C is wrong because the positive direction is tied to the incident light, not to where the centre of curvature happens to lie — that would give convex and concave mirrors opposite conventions.
MCQ 4Direct ApplicationPractice
An object is placed at a distance of magnitude 3.00 × 10⁻¹ m from a concave mirror of focal length of magnitude 2.00 × 10⁻¹ m. Using the mirror formula, the image distance v is
Show answer and why every option is right or wrong
Answer: A. A is correct. With u = −3.00 × 10⁻¹ m and f = −2.00 × 10⁻¹ m, 1/v = 1/f − 1/u = −5.00 + 3.33 = −1.67 m⁻¹, giving v = −6.00 × 10⁻¹ m. The formula and convention are in NCERT Class 12 Physics Chapter 9, printed pages 222–223.
Why B is wrong: B is wrong because it drops the negative signs on u and f and so reports a virtual image behind a concave mirror for an object outside the focus — the sign-convention error this topic turns on.
Why C is wrong: C is wrong because it comes from adding the reciprocals as 1/v = 1/f + 1/u = −5.00 − 3.33 = −8.33 m⁻¹, i.e. moving 1/u across the equals sign without changing its sign.
Why D is wrong: D is wrong because it combines both errors: the reciprocals are mishandled and the resulting sign is then dropped.
MCQ 5Direct ApplicationPractice
For a given mirror and object position, the mirror formula yields a positive value of v. This tells you that the image is
Show answer and why every option is right or wrong
Answer: C. C is correct. Positive v places the image on the side away from the incident light, behind the mirror, where no light actually converges — so the image is virtual. This follows from the convention in NCERT Class 12 Physics Chapter 9, printed page 222.
Why A is wrong: A is wrong because an image in front of the mirror corresponds to negative v under this convention, not positive.
Why B is wrong: B is wrong because 'behind the mirror' is correctly read off from the positive sign, but no light reaches there after reflection, so the image cannot be real.
Why D is wrong: D is wrong because it pairs the right character (virtual) with the wrong location; virtual images from a mirror lie behind it.
MCQ 6Concept TrapPractice
A student solving a concave-mirror problem writes u = +2.5 × 10⁻¹ m for a real object and f = +1.0 × 10⁻¹ m, then applies 1/v + 1/u = 1/f correctly and obtains a positive v. The error in this work is that
Show answer and why every option is right or wrong
Answer: D. D is correct. A real object lies on the incident-light side, so u is negative; a concave mirror's focus lies on the same side, so f is negative too. Entering both as positive is the sign-convention error, and it produces a spurious virtual image. See NCERT Class 12 Physics Chapter 9, printed page 222.
Why A is wrong: A is wrong because the mirror formula applies to concave and convex mirrors alike; only the sign of f differs between them.
Why B is wrong: B is wrong because 1/v − 1/u = 1/f is the thin lens relation; the mirror formula adds the reciprocals whatever the mirror's shape.
Why C is wrong: C is wrong because it fixes f but leaves u positive, which would put the object behind the mirror — not the arrangement described.
MCQ 7Direct ApplicationPractice
An object is placed 1.0 × 10⁻¹ m in front of a concave mirror whose focal length has magnitude 1.5 × 10⁻¹ m. The image distance v is
Show answer and why every option is right or wrong
Answer: B. B is correct. With u = −1.0 × 10⁻¹ m and f = −1.5 × 10⁻¹ m, 1/v = 1/f − 1/u = −6.67 + 10.0 = +3.33 m⁻¹, so v = +3.0 × 10⁻¹ m — positive, hence virtual. The object lies inside the focal length, which is what flips the sign. Formula and convention: NCERT Class 12 Physics Chapter 9, printed pages 222–223.
Why A is wrong: A is wrong because it comes from 1/v = 1/f + 1/u = −6.67 − 10.0 = −16.7 m⁻¹, mishandling the rearrangement, and then reports a real image where the correct sign gives a virtual one.
Why C is wrong: C is wrong because it assumes a concave mirror must give a real image and reports a magnitude with a forced negative sign; for an object inside the focus the computed v is positive.
Why D is wrong: D is wrong because the magnitude is that of the mis-rearranged calculation, paired here with the correct 'virtual' label by guesswork rather than from the sign of v.
MCQ 8CalculationPractice
A convex mirror of focal length of magnitude 2.0 × 10⁻¹ m forms an image of an object placed in front of it. The image distance has magnitude 1.2 × 10⁻¹ m. The object distance u is
Show answer and why every option is right or wrong
Answer: C. C is correct. A convex mirror has f = +2.0 × 10⁻¹ m and forms a virtual image, so v = +1.2 × 10⁻¹ m. Then 1/u = 1/f − 1/v = 5.0 − 8.33 = −3.33 m⁻¹, giving u = −3.0 × 10⁻¹ m — negative, as a real object must be. Convention: NCERT Class 12 Physics Chapter 9, printed page 222.
Why A is wrong: A is wrong because it has the right magnitude but a positive sign, placing the object behind the mirror — the sign-dropping error this topic turns on.
Why B is wrong: B is wrong. Taking v as negative (a real image) gives 1/u = 5.0 + 8.33 = 13.3 m⁻¹ and u ≈ +7.5 × 10⁻² m, not −8.0 × 10⁻² m, and neither describes this mirror. A convex mirror forms a virtual image, v = +0.12 m, so 1/u = 5.0 − 8.33 = −3.33 m⁻¹ and u = −0.30 m.
Why D is wrong: D is wrong because it both mis-signs v and reports a positive u, so neither the magnitude nor the sign survives the convention.
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Mirror Formula: quick recall before you leave
How do you solve a Mirror Formula question? A worked example
- 1
Given.
A concave mirror of focal length of magnitude 1.20 × 10⁻¹ m. An object placed in front of it at a distance of magnitude 4.00 × 10⁻¹ m from the pole.
- 2
Required.
The image distance
v, with its sign, and whether the image is real or virtual. - 3
Concept.
The mirror formula relates the three signed distances measured from the pole. The sign of the computed
vis the answer to the real-or-virtual question; it is not decided beforehand. - 4
Formula.
1/v + 1/u = 1/f. - 5
Substitution.
Fix the signs first. The object is in front of the mirror, on the incident-light side, so
u = −4.00 × 10⁻¹ m. The mirror is concave, so its focus is on the same side as the object:f = −1.20 × 10⁻¹ m.
Rearranging:1/v = 1/f − 1/u = (1 / −1.20 × 10⁻¹) − (1 / −4.00 × 10⁻¹). - 6
Calculation.
1/v = −8.333 m⁻¹ + 2.500 m⁻¹ = −5.833 m⁻¹, sov = −1.714 × 10⁻¹ m.
The1in each reciprocal is a counting number and the rearrangement introduces no measured quantity, so neither limits precision. Both given distances carry three significant figures, so the answer is quoted to three. - 7
Final answer.
v = −1.71 × 10⁻¹ m. The negative sign places the image in front of the mirror, on the same side as the object — the image is real. - 8
Common trap.
Entering
uandfas positive magnitudes. That yields1/v = 8.333 − 2.500 = 5.833 m⁻¹andv = +1.71 × 10⁻¹ m— the same magnitude with the opposite sign, which would be read as a virtual image behind a concave mirror for an object well outside the focus. The magnitude looking right is exactly what makes this error survive a quick check. Fix the signs before the arithmetic, not after. - 9
Similar NEET-style question.
A concave mirror of focal length of magnitude 1.50 × 10⁻¹ m forms a real image at a distance of magnitude 6.00 × 10⁻¹ m from the pole. Find the object distance with its sign. *(Answer:
u = −2.00 × 10⁻¹ m.)*
What to remember before solving Mirror Formula questions
Formula
Magnification by mirror
m = -v/u = h_image/h_object. Negative m: inverted image. |m| > 1: magnified; |m| < 1: diminished.
-- NCERT Class 12 Physics, Ch. 9, p. 226Which Mirror Formula formulas do you need for NEET?
1 formula — click to collapse
Mirror formula
Spherical mirror formula. Sign convention: distances from pole, positive in direction of incident light.
| Symbol | Quantity | SI Unit |
|---|---|---|
| v | image distance | m |
| u | object distance | m |
| f | focal length | m |
| m | magnification | - |
Valid when
- Spherical mirror, paraxial rays
- Sign convention used consistently
Where do students lose marks on Mirror Formula?
These are the exact patterns that cause wrong answers in NEET. Each trap includes when it triggers and how to avoid it.
2 items — click to collapse
Category: Sign Convention
Student inverts the sign of u, v, or f in mirror/lens formulas. Convention: distances measured from pole/optical centre; positive in direction of light propagation.
When it triggers
Mirror or lens problem requiring formula application.
How to avoid
Cartesian sign convention: pole at origin; light travels in +x direction; distances measured along axis are signed. Concave mirror f<0 on convention where light incident from left (or vice versa per text). Apply ONE convention throughout.
Root cause: sign error
Correction
Use Cartesian convention consistently: pole/optical-centre at origin, light travels in +x direction. Object usually has u < 0 (left of pole). Concave mirror f < 0 (most conventions). Apply ONE convention throughout.
More in Optics: 7 exam traps and mistakes · 10 formulas · 7 question patterns from its other lessons.
Mirror Formula questions from past NEET papers
No question in our NEET 2020–2025 set targets this topic directly.
Sources
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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