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How to measure a focal length

Task-oriented. You know what a focal length is and want a number.

Converging lens (+50 mm, +100 mm): the distant-source method​

The trick: light from a far-away source arrives as (almost) parallel rays, and parallel rays meet exactly in the focal point.

  1. Point the lens at something far away and bright — the window scene, or a ceiling lamp across the room. At least a few metres of distance.
  2. Hold a piece of paper (the "screen") behind the lens, parallel to it.
  3. Move the paper towards/away from the lens until a small, sharp image of the source appears (the window scene will be tiny and upside-down).
  4. Measure the lens-to-paper distance with the ruler. That distance is f.

Expected: ≈ 50 mm and ≈ 100 mm for the CoreBox lenses (the printed value, within a few millimetres).

More precise (Sek II): the lens-equation method

Use a nearby light source instead, measure object distance gg and image distance bb for three different positions, and compute ff from 1f=1g+1b\frac{1}{f} = \frac{1}{g} + \frac{1}{b} each time. Plotting 1/b1/b against 1/g1/g gives a straight line with intercepts 1/f1/f — a nice measurement exercise.

Diverging lens (−50 mm): combine it with a known lens​

A diverging lens never forms an image on a screen (its focus is virtual), so measure it indirectly:

  1. Hold the +50 mm and the −50 mm lens directly together and repeat the distant-source method.
  2. For thin lenses in contact the powers add:

1fcombo=1f1+1f2=150+1−50=0\frac{1}{f_\text{combo}} = \frac{1}{f_1} + \frac{1}{f_2} = \frac{1}{50} + \frac{1}{-50} = 0

Zero power — the pair behaves like a flat window: no image forms at any distance. That's your proof the negative lens really has ≈ −50 mm. 3. For an actual number, pair the −50 mm with the +100 mm lens instead. Ideally the combination has fcombo=(1100−150)−1=−100f_\text{combo} = \left(\frac{1}{100} - \frac{1}{50}\right)^{-1} = -100 mm — still diverging. Pairing it with a stronger positive lens than +50 mm would give a measurable real focus; within the CoreBox, the window-pane experiment in step 2 is the clean result.

Quick sanity check without any setup​

Look through the lens at text and pull it away from the page:

  • The distance where the magnified image blurs and flips upside-down ≈ the focal length of a converging lens.
  • If it never flips and never magnifies → it's the diverging lens.