Determination of the Focal Length of a Convex Lens

Using source–lens distance S0 and lens–screen distance Si

1. Objective

To determine the focal length (f) of a convex (converging) lens using measured values of the source–lens distance S0 and the lens–screen distance Si.

2. Theory

A convex lens converges rays of light and can form a sharp, real, inverted image of an object on a screen. The distances satisfy the thin lens formula:

1/f = 1/S0 + 1/Si

where:

  • S0: distance from the object (light source) to the lens
  • Si: distance from the lens to the screen (image)
  • f: focal length of the convex lens

The magnification of the image is given by:

m = Si / S0

3. Apparatus

  • Convex (converging) lens with lens holder
  • Illuminated object or object pin
  • Screen
  • Optical bench
  • Meter scale or measuring tape

4. Procedure

  1. Fix the convex lens vertically on the optical bench using a lens holder.
  2. Place the illuminated object at a known distance S0 from the lens.
  3. Move the screen along the bench until a sharp, clear, inverted image is obtained on the screen.
  4. Measure and record:
    • S0 – source–lens distance (in cm)
    • Si – lens–screen distance (in cm)
  5. Repeat the steps for at least 5–7 different values of S0.
  6. Use the thin lens formula to calculate the focal length f for each trial.
  7. Plot a graph of 1/Si (y-axis) versus 1/S0 (x-axis).
  8. Determine the focal length from the data and from the graph.

5. Interactive Data Table and Graph

Use this interactive table to enter your measured values of S0 and Si. The tool will automatically calculate 1/S0, 1/Si, and the focal length f for each trial, then draw a graph of 1/Si versus 1/S0.

Trial S0 (cm) Si (cm) 1/S0 (cm⁻¹) 1/Si (cm⁻¹) f (cm)

Graph: 1/Si vs 1/S0

6. Analysis and Result

For each row of data, the focal length is calculated from the thin lens formula:

f = 1 / (1/S0 + 1/Si)

The program computes the focal length for each valid trial and then finds the average focal length. It also performs a linear regression on the 1/Si vs 1/S0 data to estimate the intercept, which should be close to 1/f.

In a typical setup, the focal length of a standard convex lens may be around 15 cm, but the exact value depends on your measured data.

7. Scientific Interpretation for Students

  • Convex lenses converge parallel light rays to a focal point on the other side of the lens.
  • The relationship between S0 and Si is governed by the thin lens formula, not by guesswork.
  • The graph of 1/Si versus 1/S0 provides an experimental verification of geometrical optics.
  • Knowledge of focal length is essential for designing microscopes, telescopes, cameras, and eyeglasses.
  • Differences between the theoretical and experimental values of f may arise from measurement errors, lens imperfections, or misalignment.

8. Notes for Good Practice

  • Ensure that the lens, object, and screen are all at the same height and along the same straight line.
  • Adjust the screen slowly near the sharp image position for better accuracy.
  • Take multiple readings and avoid using data that clearly does not agree with the general pattern.