Pick up any spoon and look at your reflection in its bowl-shaped inner surface. You will see yourself upside down, smaller, and inverted. That curved, inward-reflecting surface is precisely what physicists call a concave mirror — and it is one of the most fascinating and practically useful optical instruments in science. From a dentist's examination mirror to a car headlight reflector, from a satellite dish to the mirror of a reflecting telescope, the concave mirror is everywhere.
In school physics, the concave mirror is the centrepiece of the Reflection of Light chapter (CBSE Class 10, Chapter 10) and a key instrument in the Class 12 optics practical syllabus. Students study the mirror formula (1/f = 1/v + 1/u), draw ray diagrams for six standard object positions, and conduct the experiment to determine the focal length of a concave mirror using an illuminated object and a screen on an optical bench.
This guide covers the concave mirror completely: key terms (pole, centre of curvature, principal focus, focal length), the New Cartesian Sign Convention for mirrors, the mirror formula and magnification, six image formation cases with descriptions, the step-by-step experiment procedure, observation table, uses, and a full comparison with convex mirrors. All apparatus described is manufactured and supplied by AJKANT Overseas from Ambala, India.
(Negative for concave mirror)
Unit: cm or m
(from pole of mirror)
Unit: cm or m
(always negative)
Unit: cm or m
- 1. What is a Concave Mirror? Key Terms
- 2. New Cartesian Sign Convention for Mirrors
- 3. Mirror Formula, Magnification, and Radius of Curvature
- 4. Ray Diagrams — 6 Image Formation Cases
- 5. Apparatus Required for the Experiment
- 6. Experiment Procedure — Step-by-Step
- 7. Observation Table
- 8. Uses of Concave Mirror
- 9. Concave Mirror vs. Convex Mirror
- 10. Frequently Asked Questions (FAQ)
1. What is a Concave Mirror? Key Terms
A concave mirror (also called a converging mirror) is a spherical mirror whose reflecting surface is curved inward — like the inside of a hollow sphere. When parallel rays of light fall on a concave mirror, they reflect and converge to meet at a point in front of the mirror called the principal focus. This converging behaviour makes the concave mirror one of the most versatile optical instruments.
2. New Cartesian Sign Convention for Mirrors
All distances in mirror optics are measured from the pole (P) of the mirror. The New Cartesian Sign Convention must be followed consistently:
3. Mirror Formula, Magnification, and Radius of Curvature
1/v = 1/f − 1/u = 1/(−15) − 1/(−30) = −1/15 + 1/30 = −2/30 + 1/30 = −1/30
∴ v = −30 cm (real, inverted image at the same distance as the object — object is at C)
|m| > 1 → Magnified | |m| = 1 → Same size | |m| < 1 → Diminished
Example: v = −30 cm, u = −30 cm → m = −(−30)/(−30) = −1 (real, inverted, same size)
Example: If R = 30 cm, then f = 15 cm.
4. Ray Diagrams — Six Image Formation Cases for a Concave Mirror
| Case | Object Position | Image Position | Image Nature | Use Case / Application |
|---|---|---|---|---|
| Case 1 | At infinity (u = ∞) | At focus F (v = −f) | Real, inverted, highly diminished (point image) | Used to find focal length by distant-object method. Solar concentrator. |
| Case 2 | Beyond C (u > 2f) | Between F and C (f < |v| < 2f) | Real, inverted, diminished | Camera with concave mirror objective. Rear-view mirrors (not applicable — see convex) |
| Case 3 | At C (u = 2f) | At C (v = 2f) | Real, inverted, same size as object | Used in the experiment to verify the formula. Medical/dental examination. |
| Case 4 | Between C and F (f < u < 2f) | Beyond C (|v| > 2f) | Real, inverted, magnified | Projector using concave mirror. Searchlight reflector. |
| Case 5 | At F (u = f) | At infinity (v = ∞) | Real, inverted, infinitely large (parallel beam) | Torch/flashlight, car headlight, searchlight (source placed at F gives parallel beam) |
| Case 6 | Between F and P (u < f) | Behind mirror (v > 0, positive) | Virtual, erect, magnified | Shaving/makeup mirror. Dentist’s examination mirror. ENT doctor’s mirror. |
- A ray parallel to the principal axis reflects through the principal focus F.
- A ray passing through the centre of curvature C reflects back along the same path (it hits the mirror normally).
- A ray directed towards the pole P reflects such that the angle of incidence = angle of reflection (with the principal axis as the normal at P).
5. Apparatus Required for the Experiment
6. Experiment Procedure — Step-by-Step
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Find Rough Focal Length by Distant Object MethodHold the concave mirror facing a bright distant window or a far light source. Hold a white card in front of the mirror and move it back and forth until a small, sharp, bright spot (image of the distant source) forms on the card. The distance from the mirror pole to the card is approximately equal to the focal length f. Note this rough value to set up the optical bench ranges for u.
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Mount the Mirror, Object, and Screen on the Optical BenchMount the concave mirror at the far end of the optical bench (facing the object). Mount the illuminated crosswire object on a rider. Mount the white screen on a rider between the object and the mirror. Ensure all components are at the same height and on the principal axis (centres aligned). Switch on the crosswire lamp.
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Set Object Distance to u = 2.5f (First Reading)Set the object at a distance u = 2.5f from the mirror pole (object beyond C). For f = 15 cm, set u = 37.5 cm. Record the bench-scale positions of object (x₀) and mirror (x₁). u = x₁ − x₀ (magnitude). In sign convention: u = −|object distance|.
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Move Screen to Find the Sharpest ImageSlide the white screen along the bench (between the object and the mirror) until the sharpest, most detailed image of the crosswire appears on the screen. The image is sharpest when it is smallest and most defined. Record the screen position x₂. Image distance: v = −|x₁ − x₂| (negative because image is in front of mirror).
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Calculate f from Mirror FormulaApply the mirror formula: 1/f = 1/v + 1/u (with both u and v negative for a real image from a concave mirror). Calculate f for this reading. Alternatively use: f = uv / (u + v). Record the calculated focal length fᵢ in the observation table.
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Repeat for 4–5 More Object DistancesMove the object to new distances: u = 3f, 2f, 1.5f, 1.2f. For each position, find the sharpest screen image and record u, v, and calculated f. Do NOT set u < f — the concave mirror forms no real image when the object is inside the focal length (it forms a virtual image behind the mirror that cannot be caught on a screen).
7. Observation Table
Rough focal length: f₀ ≈ ______ cm | Least count of optical bench: 0.1 cm
| S.No. | Object Position x₀ (cm) |
Mirror Position x₁ (cm) |
Screen Position x₂ (cm) |
Object Dist. u = −(x₁−x₀) |
Image Dist. v = −(x₁−x₂) |
f = uv/(u+v) (cm) |
|---|---|---|---|---|---|---|
| 1 | ____ | ____ | ____ | ____ | ____ | ____ |
| 2 | ____ | ____ | ____ | ____ | ____ | ____ |
| 3 | ____ | ____ | ____ | ____ | ____ | ____ |
| 4 | ____ | ____ | ____ | ____ | ____ | ____ |
| 5 | ____ | ____ | ____ | ____ | ____ | ____ |
| Mean focal length f̄ = | ____ cm | |||||
Precautions for the Concave Mirror Experiment
- Paraxial rays only: The object must be small and placed close to the principal axis so only paraxial (near-axis) rays hit the mirror. Wide rays hitting the mirror edges cause spherical aberration and give a blurred image.
- Mirror must be vertical: Mount the mirror perpendicular to the optical bench. A tilted mirror deflects the image off-axis and the screen cannot intercept it correctly.
- Avoid parallax error: When locating the image on the screen, ensure you view the screen perpendicularly. The image should be in the same plane as the screen — test for zero parallax by moving your eye side to side while adjusting the screen.
- Bright, well-defined object: Use a bright illuminated crosswire for a sharp, well-defined image. Dim objects give blurry images that are hard to locate precisely.
- Keep u greater than f: Never set the object inside the focal length in this experiment — no real image is formed and the screen search is fruitless.
8. Uses of Concave Mirror
9. Concave Mirror vs. Convex Mirror
- Reflecting surface curves inward (like inside of a bowl)
- Focal length: negative (in front of mirror)
- Converges parallel light rays to the principal focus
- Forms real AND virtual images depending on object position
- Can magnify or diminish the image
- Field of view: narrow (limited to object in front)
- Uses: torches, headlights, shaving mirrors, dentist’s mirrors, solar cookers, telescopes
- Image orientation: Inverted (real) or erect (virtual)
- Reflecting surface curves outward (like outside of a ball)
- Focal length: positive (behind mirror, virtual)
- Diverges parallel light rays (they appear to come from the virtual focus)
- Forms only virtual, erect, diminished images
- Always diminishes the image (|m| < 1 always)
- Field of view: wide (shows a larger area of the scene)
- Uses: rear-view mirrors in vehicles, security mirrors in shops, road safety mirrors at blind corners
- Image orientation: Always erect
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10. Frequently Asked Questions (FAQ)
The mirror formula for any spherical mirror (concave or convex) is: 1/f = 1/v + 1/u, where f is the focal length, v is the image distance (from the pole), and u is the object distance (from the pole). For a concave mirror, in the New Cartesian Sign Convention, f is negative, u is always negative (object in front of mirror), and v is negative for real images (in front of mirror) and positive for virtual images (behind mirror). The formula can be rearranged as: f = uv / (u + v) which is convenient for calculating f from experimental measurements of u and v.
The focal length of a concave mirror is found experimentally by two methods: (1) Distant object method: Hold the concave mirror facing a distant bright object (effectively at infinity). Hold a white card screen in front and move it until a sharp, small image forms. The mirror-to-screen distance is approximately equal to f. (2) Optical bench method (accurate): Place the illuminated object at different known distances u from the mirror on an optical bench. For each u, find the position of the screen where a sharp image is formed (image distance v). Calculate f using 1/f = 1/v + 1/u. Take the mean of f from 5-6 different object positions. This gives the experimental focal length.
The relationship between focal length (f) and radius of curvature (R) of a spherical mirror is: R = 2f, or equivalently f = R/2. This means the focal length is exactly half the radius of curvature. Geometrically, this is because the principal focus F is the midpoint of the line segment PC (from pole P to centre of curvature C). This relationship holds for both concave and convex mirrors. In the experiment, if you measure f = 15 cm, then R = 30 cm, meaning the mirror is a segment of a sphere of radius 30 cm.
A concave mirror forms a virtual, erect, and magnified image only when the object is placed between the focus (F) and the pole (P) of the mirror, i.e., when the object distance u is less than the focal length f. In this case, the reflected rays diverge and appear to come from a point behind the mirror when extended backward — forming a virtual image that cannot be caught on a screen. This is the principle of the shaving mirror, makeup mirror, and dentist’s examination mirror. For all other object positions (beyond F), a concave mirror forms real, inverted images.
A concave mirror is used in a torch because of Case 5: when a light source (bulb or LED) is placed exactly at the principal focus (F) of a concave mirror, all the diverging rays from the source hit the concave mirror and reflect as a parallel beam directed forward. This parallel beam travels long distances without spreading out, producing a strong, focused beam of light. A convex mirror cannot be used for this purpose because it diverges light rays (it is a diverging mirror), and placing a light source at its virtual focus would not produce a useful parallel beam — the reflected rays would spread outward in all directions.
Source Optics Lab Equipment from Ambala
AJKANT Overseas manufactures and supplies complete optics lab kits — concave mirrors, convex mirrors, optical benches, lens and mirror holders, illuminated crosswire object boxes, white screens, and prism sets — for CBSE Class 10 and Class 12 physics practicals. Factory-direct from Ambala, India. Bulk supply for schools, colleges, and government tenders across India and 25+ countries.
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