Light is the medium through which we perceive our world, and the convex lens is the most important optical instrument that shapes how we interact with light — in eyeglasses, cameras, microscopes, telescopes, projectors, and magnifying glasses. Understanding how a convex lens forms images and how to measure its focal length is a central topic in both CBSE Class 10 (Light: Reflection and Refraction) and Class 12 (Ray Optics) physics syllabi.
The focal length of a convex lens is the distance between the lens centre and its principal focus — the point where a beam of parallel light rays converges after passing through the lens. A shorter focal length means a more powerful (more curved) lens; a longer focal length means a weaker (less curved) lens. This relationship is captured in the power of a lens: P = 1/f (in dioptres when f is in metres).
This guide covers everything about the focal length of convex lens: the definition and sign convention, the thin lens formula (1/f = 1/v − 1/u), five ray diagram cases, the step-by-step experiment procedure (both direct and displacement methods), observation table, calculations, uses of convex lenses, and a complete comparison with concave lenses. All optics apparatus described is manufactured by AJKANT Overseas from Ambala, India.
Unit: cm or m
(from optical centre)
Unit: cm or m
(always negative in NCCS)
Unit: cm or m
Unit: Dioptre (D)
f in metres
- 1. What is Focal Length of a Convex Lens?
- 2. New Cartesian Sign Convention for Lenses
- 3. Lens Formula and Power of a Lens
- 4. Ray Diagrams — 5 Standard Cases
- 5. Apparatus Required
- 6. Experiment Procedure — Step-by-Step
- 7. Displacement Method for Focal Length
- 8. Observation Table
- 9. Uses of Convex Lens
- 10. Convex Lens vs. Concave Lens
- 11. Frequently Asked Questions (FAQ)
1. What is Focal Length of a Convex Lens?
A convex lens (also called a converging lens) is a transparent optical element that is thicker at the centre than at the edges. When parallel rays of light pass through a convex lens, they are refracted (bent) and converge to meet at a single point called the principal focus (F). The distance from the optical centre (O) of the lens to the principal focus is called the focal length (f) of the lens.
Key properties of the focal length of a convex lens:
- Sign: The focal length of a convex lens is positive in the New Cartesian Sign Convention (since the focus is on the same side as the refracted light — the right side for a lens with light coming from the left).
- Units: Centimetres (cm) in practical work; metres (m) for power calculation.
- Value range for school lenses: Typically 10 cm, 15 cm, 20 cm, or 25 cm for convex lenses supplied in school physics labs.
- Relationship to curvature: A more curved lens has a shorter focal length and is more powerful. A less curved lens has a longer focal length and is weaker.
2. New Cartesian Sign Convention for Lenses
All measurements in lens optics follow the New Cartesian Sign Convention, which must be applied consistently when using the lens formula:
3. Lens Formula and Power of a Lens
1/v = 1/f + 1/u = 1/20 + 1/(−30) = 1/20 − 1/30 = 3/60 − 2/60 = 1/60
∴ v = +60 cm (real, inverted image on the other side of the lens)
Convex lens (f positive) → P is positive | Concave lens (f negative) → P is negative
Example: f = 20 cm = 0.20 m → P = 1/0.20 = +5 D
|m| > 1 → Magnified | |m| < 1 → Diminished | |m| = 1 → Same size as object
4. Ray Diagrams — 5 Standard Cases for a Convex Lens
| Case | Object Position | Image Position | Image Nature | Application |
|---|---|---|---|---|
| Case 1 | At infinity (u = ∞) | At focus F (v = +f) | Real, inverted, highly diminished (point) | Used to find focal length directly (sun/distant object method) |
| Case 2 | Beyond 2F (u > 2f) | Between F and 2F (f < v < 2f) | Real, inverted, diminished | Camera lens, human eye |
| Case 3 | At 2F (u = 2f) | At 2F (v = 2f) | Real, inverted, same size | Photocopier at 1:1 magnification |
| Case 4 | Between F and 2F (f < u < 2f) | Beyond 2F (v > 2f) | Real, inverted, magnified | Slide projector, movie projector, film enlarger |
| Case 5 | Between F and O (u < f) | Same side as object (v negative) | Virtual, erect, magnified | Magnifying glass, reading lens, simple microscope |
📷 Standard Ray Diagram: Object at 2F (Case 3)
Three standard rays used in convex lens ray diagrams:
- A ray parallel to the principal axis refracts and passes through the far focal point F′.
- A ray passing through the optical centre O passes through undeviated (no bending at the centre).
- A ray directed towards the near focal point F refracts and emerges parallel to the principal axis.
The point where any two of these three refracted rays intersect is the image point for the tip of the object.
5. Apparatus Required
6. Experiment Procedure — Step-by-Step
Method 1: Standard Object-Image Method (Lens Formula Method)
-
Rough Focal Length by Distant Object MethodHold the convex lens facing a bright, distant object (a window, a far lamp, or the Sun — never look at the Sun directly). Hold a white card on the other side and move it until a sharp, small, inverted image forms. The card distance from the lens is an approximate focal length f₀. This gives you the approximate working range for u in the next steps.
-
Mount Components on the Optical BenchClamp the illuminated object at one end of the optical bench. Mount the convex lens at the centre on a lens holder rider. Mount the white screen on a rider at the far end. Ensure all three are aligned: centres of object, lens, and screen must be at the same height and on the principal axis of the lens.
-
Set Object Distance u (First Reading: u = 2.5f)Set the object at a distance u = 2.5f from the lens centre (e.g., if f ≈ 15 cm, set u ≈ 37.5 cm, so the object is beyond 2F). Note the positions of the object (x₀) and lens (x₁) on the bench scale. u = x₁ − x₀. In sign convention: u = −(x₁ − x₀).
-
Find the Sharp Image by Moving the ScreenMove the screen along the bench on the other side of the lens until the sharpest, clearest image of the illuminated object appears on the screen. The image is sharpest when it is smallest (for a point object) or most detailed (for an arrow/crosswire object). Note the screen position (x₂). v = x₂ − x₁.
-
Calculate f from the Lens FormulaApply the lens formula: 1/f = 1/v − 1/u (using sign convention: u is negative, v is positive for real image). Calculate fᵢ for this reading and enter in the observation table.
-
Repeat for 5 Different Object DistancesMove the object to new positions (e.g., u = 3f, 2f, 1.7f, 1.5f, 1.2f) and repeat steps 3–5 for each. Do NOT set u < f — no real image forms when the object is inside the focal length. Record u, v, and calculated f for each position.
7. Displacement Method for Focal Length (More Accurate)
The displacement method (also called the conjugate foci method) eliminates the need to locate the optical centre of the lens precisely, making it more accurate than the standard method for lenses with significant thickness.
Procedure: Fix the object and screen at a separation D (> 4f). Move the lens between them — there will be TWO positions of the lens that give a sharp image. Measure the separation d between these two lens positions. Substitute in the formula.
8. Observation Table
Approximate focal length (rough estimate): f₀ ≈ ______ cm | Least count of optical bench: 0.1 cm
| S.No. | Object Position x₀ (cm) | Lens Position x₁ (cm) | Screen Position x₂ (cm) | u = −(x₁−x₀) (cm) | v = x₂−x₁ (cm) | f = uv/(u+v) (cm) |
|---|---|---|---|---|---|---|
| 1 | ____ | ____ | ____ | ____ | ____ | ____ |
| 2 | ____ | ____ | ____ | ____ | ____ | ____ |
| 3 | ____ | ____ | ____ | ____ | ____ | ____ |
| 4 | ____ | ____ | ____ | ____ | ____ | ____ |
| 5 | ____ | ____ | ____ | ____ | ____ | ____ |
| Mean focal length f̄ = | ____ cm | |||||
9. Uses of Convex Lens
10. Convex Lens vs. Concave Lens
- Thicker at centre, thinner at edges
- Converges (bends inward) parallel light rays
- Focal length: positive (+f)
- Power: positive (+P)
- Forms real + virtual images (depending on object position)
- Can magnify or diminish the image
- Uses: spectacles for hypermetropia, cameras, microscopes, magnifying glasses, projectors
- V-I characteristic: focal point on the far side of lens from object
- Thinner at centre, thicker at edges
- Diverges (bends outward) parallel light rays
- Focal length: negative (−f)
- Power: negative (−P)
- Forms only virtual, erect, diminished images
- Always diminishes the image (|m| < 1 always)
- Uses: spectacles for myopia (short-sightedness), Galilean telescopes, camera viewfinders
- Focal point is on the same side as the object (virtual focus)
Explore Related Physics Lab Instruments & Guides
11. Frequently Asked Questions (FAQ)
The lens formula (thin lens formula) for any lens is: 1/f = 1/v − 1/u, where f is the focal length, v is the image distance from the optical centre, and u is the object distance from the optical centre. For a convex lens, f is positive. The sign convention is the New Cartesian Sign Convention: object distance u is always negative (object to the left), and image distance v is positive for a real image (right side) and negative for a virtual image (left side). The formula can be rearranged to find f from any pair of (u, v) values: f = uv/(u + v) (using magnitudes, careful with signs).
The distant object method is the quickest way to find the approximate focal length of a convex lens: (1) Hold the convex lens facing a bright, distant object (at least 10 metres away — a window, a tree, or a light source). (2) Hold a white card on the other side of the lens. (3) Move the card back and forth until a sharp, small, inverted image of the distant object forms on the card. (4) Measure the distance from the lens centre to the card. This distance is approximately equal to the focal length f. This works because a very distant object is effectively at infinity, and light from infinity converges at the focal point.
Power of a lens P = 1/f, where f is in metres. For f = 20 cm = 0.20 m: P = 1/0.20 = +5 Dioptres (D). The positive sign confirms it is a convex (converging) lens. A concave lens of focal length 20 cm would have P = −5 D. Dioptres are the standard unit for optician prescriptions — when an optician prescribes +2.5 D, they mean a convex lens with focal length 1/2.5 = 0.4 m = 40 cm.
When the object is placed between the focus (F) and the optical centre (O) of a convex lens (u < f), the lens forms a virtual, erect, and magnified image on the same side as the object (v is negative, image is to the left). This is the principle of the magnifying glass. The image cannot be caught on a screen (because it is virtual); it can only be seen by looking through the lens. The magnification m = v/u is positive (erect) and |m| > 1 (magnified).
The key difference is in the sign of the focal length: a convex (converging) lens has a positive focal length (+f) because its focus is on the real side (where refracted light goes), while a concave (diverging) lens has a negative focal length (−f) because its focus is virtual (on the same side as the incident light). In terms of physical measurement, the focal length of a concave lens cannot be measured directly by the screen-and-bench method (since it forms no real image) — it must be measured indirectly by combining it with a known convex lens.
Source Optics Lab Equipment from Ambala
AJKANT Overseas manufactures and supplies complete optics lab kits — convex and concave lenses, optical benches, lens holders, illuminated object boxes, 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.
Request Optics Lab Kit Quote →