Focal Length of Convex Lens using u-v Method
What you will learn
Determine the focal length of a thin convex lens by finding the image distance (v) for various object distances (u) on an optical bench, removing parallax.
Materials needed
- Optical Bench (2 meters long with graduated scale)What is it?Optical Bench (2 meters long with graduated scale)₹50
Dual-rail brass and cast iron optical bench with engraved millimeter graduations.
Specifications- Length
- 1.5 meter / 150 cm
- Scale Resolution
- 1 mm divisions with vernier to 0.1 mm
- Uprights Included
- 4 sliding uprights with slow-motion rack
- Material
- Heavy cast iron bed, machined steel rails
- Biconvex Lens mounted on upright holderWhat is it?Biconvex Lens mounted on upright holder₹95
Double convex optical glass lens with high-quality polished spherical surfaces.
Specifications- Nominal Focal Length
- +15 cm
- Diameter
- 50 mm aperture
- Material
- Optical crown glass
- Mounting
- Spring-loaded ring clamp
- Object Optical NeedleWhat is it?Object Optical Needle₹140
Two vertical brass optical needles with fine points mounted on adjustable slider uprights.
Specifications- Length
- 12 cm
- Diameter
- 3 mm brass rod with hardened tip
- Vertical Travel
- 50 mm adjustable height
- Base Fitting
- Knurled lock-ring fitting
- Image Optical NeedleWhat is it?Image Optical Needle₹185
Standard laboratory apparatus used in Focal Length of Convex Lens using u-v Method.
Specifications- Category
- Physics Apparatus
- Grade
- CBSE / NEP 2020 Laboratory Standard
- Index Needle for measuring bench errorWhat is it?Index Needle for measuring bench error₹230
Standard laboratory apparatus used in Focal Length of Convex Lens using u-v Method.
Specifications- Category
- Physics Apparatus
- Grade
- CBSE / NEP 2020 Laboratory Standard
- Screen / Spirit LevelWhat is it?Screen / Spirit Level₹275
Standard laboratory apparatus used in Focal Length of Convex Lens using u-v Method.
Specifications- Category
- Physics Apparatus
- Grade
- CBSE / NEP 2020 Laboratory Standard
Tick items as you collect them. Tap + to see the product, specifications and buy options.
Stay safe
- Tips of the object needle, lens optical center, and image needle must lie along the same horizontal axis.
- Parallax must be completely eliminated between the real inverted image and the image needle.
- Object needle must always remain beyond the principal focus (u > f).
- Account for index correction for precise distances.
Steps
- 1Level the optical bench horizontally using the leveling screws and spirit level.Observation
Optical bench leveling screws adjusted with spirit level so bench rails are strictly horizontal.
SafetyDo not drop heavy cast-iron optical uprights onto bench brass scales.
- 2Obtain a rough estimate of the focal length by projecting the image of a distant tree or building on a white wall.Observation
Focus distant window image onto paper screen; rough focal length measured at approx 15 cm.
SafetyNever view the sun directly through the convex lens; intense focal heat can cause retinal burns.
- 3Mount the convex lens in the middle of the optical bench on an upright holder.Observation
Object needle tip, lens optical center, and image needle tip aligned to identical vertical height.
SafetyKeep needle tips covered with rubber caps when adjusting upright heights.
- 4Place the object needle at a distance u > 2f from the lens and illuminate it.Observation
Object needle placed at 30 cm from lens; real inverted image forms on the other side.
SafetyEnsure lens holder clamping knob is finger-tight without cracking glass edge.
- 5Place the image needle on the other side of the lens and look through the lens from a distance.Observation
Move eye sideways: image needle tip stays locked to inverted image tip without relative displacement.
SafetyMaintain 25 cm minimum distance between eye and needles to avoid eye strain.
- 6Adjust the position of the image needle until its tip coincides with the inverted tip of the object needle image without parallax.Observation
Repeat for 5 distinct object distances from 25 cm to 45 cm; all yield f = 15.0 cm.
SafetySecure all brass thumbscrews before reading vernier indexes on uprights.
- 7Note the positions of lens, object needle, and image needle to compute u and v across 6 distinct distances.
Tap + on a step to see what you will observe and any safety tips.
Record your observations
| Object Distance u (cm) | Image Distance v (cm) | u + v (cm) | Calculated f = uv/(u+v) (cm) |
|---|---|---|---|
| -25.0 cm | +37.5 cm | 62.5 cm | 15.00 cm |
| -30.0 cm | +30.0 cm | 60.0 cm | 15.00 cm (2f position) |
| -35.0 cm | +26.2 cm | 61.2 cm | 14.97 cm |
| -40.0 cm | +24.0 cm | 64.0 cm | 15.00 cm |
| -45.0 cm | +22.5 cm | 67.5 cm | 15.00 cm |
Tap a highlighted cell to write your own observation.
Result and conclusion
The focal length of the convex lens is determined to be 15.0 cm ± 0.2 cm using the lens formula 1/f = 1/v - 1/u and confirmed via the 1/u vs 1/v graph.
| Observation | What it means |
|---|---|
| Convex Lens Real Image | For object distance |u| > f, the lens produces a real, inverted image on the opposite side. |
| Symmetric 2f Condition | At u = -30.0 cm, v = +30.0 cm; image is real, inverted, exactly same size as object, confirming 2f = 30 cm, f = 15 cm. |
| Concordant Focal Length | Mean focal length across 5 independent optical bench trials is f = 15.0 ± 0.05 cm. |
| Parallax Removal | Complete absence of parallax between image and search needle confirms accurate conjugate focal alignment. |
Sample readings. Replace with your own results.