What it shows
A convex lens forms a real, inverted image on a screen at a distance that depends on where the object is. The lens formula links the two distances to the focal length, and a graph of 1/v against 1/u gives f accurately.
The science
For a thin lens, the object distance u, the image distance v and the focal length f are related by 1/v + 1/u = 1/f when all distances are taken as positive numbers for a real object and real image. If you plot 1/v against 1/u you get a straight line that cuts the two axes at 1/f, so the intercept gives f without knowing the exact position of the lens centre. When u = 2f the image is the same size as the object and v = 2f as well.
Materials
Cost: under Rs 200. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.
- A magnifying glass or a reading lens of about 10 to 20 cm focal length
- A metre rule or a long wooden strip as the optical bench
- A torch or a bright LED lamp with a cross cut in black paper as the object
- A white card or cardboard as the screen
- Clay or clothes pegs to hold the lens, object and screen upright
- A pencil, a notebook and graph paper
Safety
For this project: Never point the lens at the Sun; an adult must make the cross cut in the paper.
Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.
All the safety rulesStep by step
8 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.
Fix the lamp with its cross at the 0 cm mark of the rule and hold the lens upright on the rule with clay.
First estimate f by focusing a distant window on the card; this rough value tells you where to place the object.
Put the lens 30 cm from the object, move the screen along the rule until the cross is sharp and note the lens-to-screen distance v.
Move the lens to 25, 22, 20, 18 and 16 cm from the object and find v again each time, moving the screen back and forth to find the sharpest position.
Repeat each setting twice, from the near and the far side of focus, and use the average of v.
Make a table of u, v, 1/u and 1/v and calculate f from each pair using the lens formula, then average.
Plot 1/v against 1/u, draw the best straight line and read the intercepts on both axes.
Also plot u against v and mark the point where u = v, which is at twice the focal length.
What you should see
The 1/v against 1/u graph is a straight line with equal intercepts on both axes, and the value 1/intercept is the focal length, which agrees with the quick distant-object value to within about 1 cm.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
1State the thin lens formula.
1/v − 1/u = 1/f in sign convention, or 1/v + 1/u = 1/f using positive distances for a real image.
2Where is the image when the object is at 2f?
At 2f on the other side, real, inverted and of the same size.
3Why take readings from both sides of the sharp position?
The eye cannot judge the exact sharpest point, so averaging cancels the error.
4What do the intercepts of the graph give?
Both equal 1/f, the reciprocal of the focal length.
Take it further
Measure the magnification v / u for each position and plot it against v to find a second value of f.
Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.
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