Focal Length of a Converging Thin Lens
Place a real object at several distances d_o along the optical axis; read noisy image distances d_i and recover the unknown focal length f from the Gaussian lens law, averaged over trials.
Goal
Determine the focal length f of a fixed converging thin lens using 1/f = 1/d_o + 1/d_i with several (d_o, d_i) measurements and the sample mean of per-row estimates f_i = 1/(1/d_o + 1/d_i).
Equipment
- Optical bench (schematic)
- Converging thin lens (unknown f)
- Object on axis
- Screen / position readout with small noise
Theory
For a paraxial thin lens in air, object distance d_o, image distance d_i, and focal length f satisfy 1/f = 1/d_o + 1/d_i (Gaussian form). For a real object and a real image on the opposite side, both d_o and d_i are positive in the usual sign convention used here; rearranging gives f = d_o d_i / (d_o + d_i).
Procedure
- The bench hides a fixed converging lens; you only set the object distance d_o with the slider.
- Choose d_o well above the focal region (avoid d_o ≈ f where the image goes to infinity). Spread values across the available range.
- Press “Record measurement” to log (d_o, d_i): d_i is read with small screen-parallax / ruler noise.
- Repeat for at least 6 different object positions.
- The table adds f = 1/(1/d_o + 1/d_i) for each row. Take the sample mean of f as your result.
- Compare with the reference focal length and write the conclusion.
Experiment
Conclusion
The mean focal length agrees with the reference value within tolerance. Main uncertainties: reading d_i, parallax, assuming an ideal thin lens, and avoiding the singular region d_o ≈ f.