Illuminated arrow object
Provides a recognisable shape so image orientation and sharpness can be judged.
Physics / Convex lens focal length
FREE TO EXPLOREEXPERIMENT 06 · PHYSICS LABORATORY
Focal length of a convex lens by the u–v method
Determine the focal length of one thin convex lens using focused object–image pairs, and test the thin-lens relationship with a reciprocal-distance graph. Explore a virtual apparatus, collect readings and analyse a graph.
CHANGE · OBSERVE · MEASURE
Your virtual workbench.
FOCUSED IMAGE DISTANCE V—
MEASUREMENT STATUS
Ready for a virtual observation.
Arrow keys adjust by 0.1 cm. Find a sharp image before recording.
Adjust the apparatus, then take a reading.
Readings are generated by an ideal model. The diagram is schematic and is not to scale.
Simulation assumptions and limits
The simulation uses a monochromatic paraxial thin-lens model with a fixed 15 cm focal length. The ray diagram illustrates geometrical construction; it does not calculate diffraction, lens thickness, spherical or chromatic aberration, detector response, scattered light or actual image contrast. Focus is tested against a calculated plane with a 0.05 cm software tolerance and observations are displayed to 0.1 cm. These choices teach the measurement workflow but cannot establish real apparatus accuracy. For a real lens, identify its principal-plane approximation, assess focus range and scale uncertainty, and check alignment before interpreting agreement with the model. The lens has a model focal length of 15.0 cm and is treated as thin and paraxial. The scene is a schematic ray diagram. A screen setting within 0.05 cm of the ideal image plane is accepted; this tolerance represents half a 0.1 cm scale step, not optical depth of focus. Spherical/chromatic aberrations, lens thickness and alignment errors are omitted.
Know your apparatus.
Thin convex lens and holder
Refracts light into a real image when the object is beyond the focal point. Keep the same lens throughout the series.
Movable screen
Intercepts the image. Its location is adjusted manually until focus is achieved.
Optical bench and distance scale
Keeps object, lens and screen aligned and provides object and image distances from the lens plane.
FOLLOW THE METHOD
A reason behind every step.
Determine the focal length of one thin convex lens using focused object–image pairs, and test the thin-lens relationship with a reciprocal-distance graph. Suggested independent settings: 25, 32, 38, 45, 60 cm.
Align the bench
Place the illuminated object, lens centre and screen centre on a common axis. Establish the lens plane as the distance origin. In a physical lab, use a low-power lamp and keep the screen perpendicular to the bench.
Why this step matters
Misalignment can hide the image or make its sharpest part difficult to judge.
Choose the first object position
Keep the same lens and set u = 25.0 cm. Predict the approximate image position before moving the screen. All suggested object positions exceed the 15 cm model focal length.
Why this step matters
Selecting u > f ensures a real image is available for the screen method.
Find focus manually
Move the screen through the blurred image and bracket the sharpest position from both sides. The virtual bench accepts a reading only when the screen is within 0.05 cm of the ideal image plane; that tolerance is a software rule, not a claim about real visual precision.
Why this step matters
A lens calculation requires the actual image-plane separation, rather than any screen coordinate.
Record one observation
Record u and the focused screen distance v to 0.1 cm. Note the inverted image and its relative size. Preserve the measured numbers before calculating f.
Why this step matters
Separating observation from calculation prevents replacing measurements with desired theoretical values.
Repeat for a range of positions
Use u = 30.0, 35.0, 45.0 and 60.0 cm. Refocus for every new object position; do not leave the previous screen distance unchanged. Keep lens selection and distance units consistent.
Why this step matters
Several pairs test whether one focal length explains different image positions.
Calculate and interpret
For each pair compute f = uv/(u+v), then plot 1/v against 1/u with labelled reciprocal units. Report the fitted slope, intercept, reciprocal-intercept focal length and limitations. Distinguish rounding differences from actual evidence of experimental noise.
Why this step matters
The table and graph offer complementary checks of the model rather than a single convenient reading.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into a result.
Points are your observations. The fit uses SI x and y values before display scaling.
LINEAR FIT · y = mx + b
1/v = m(1/u) + b; m ≈ −1; f = 1/b
| # | Object distance u (cm) | Focused image distance v (cm) | Inverse object distance 1/u (m⁻¹) | Inverse image distance 1/v (m⁻¹) | Remove |
|---|
No readings yet. Take a virtual measurement and record it.
Calculate it yourself.
CHECK YOUR UNDERSTANDING