What it shows
Light passing through a second polarising filter is cut down by cos² of the angle between the two filters’ axes. Measuring the light level against the angle verifies Malus’s law.
The science
Natural light vibrates in all directions. A polariser lets through only the component of the electric field along its axis, so the transmitted intensity is half the original and the light is plane-polarised. When this passes a second polariser (the analyser) at angle θ to the first, the intensity is I = I0 cos²θ, Malus’s law. At 0 degrees the light passes fully, at 90 degrees it is almost stopped, and light from the sky or from reflections off water is partly polarised.
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.
- Three linear polarising sheets (polarising sunglass lenses, the film from an old LCD calculator or a school polarising sheet; circular 3D cinema glasses do not work well)
- A smartphone with a lux meter app (an LDR is not suitable, because its response is not in proportion to the light)
- A steady white LED lamp or a torch fixed in position
- A circular card with angles marked every 15 degrees
- A cardboard tube to block stray light
- Clay or tape for holders
Safety
For this project: An adult must take apart any old screen and remove the polarising film, handling the glass with care. Never look at the Sun through the filters.
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.
Step by step
7 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.
Set up the lamp, the first polariser and the light sensor in a straight line inside the tube, and note the lux reading with only the first polariser in place.
Add the second polariser close behind the first and rotate it until the reading is highest; call this angle 0 degrees and mark the card.
Turn the second polariser in steps of 15 degrees up to 180 degrees and read the lux value at each step.
Subtract the dark reading (lamp off) from every reading to remove stray light.
Calculate cos² θ and the ratio I / I_max for each angle in a table.
Plot I / I_max against cos² θ and see that the points lie on a straight line through the origin with slope 1.
Set the second polariser to 90 degrees so that the two are crossed, then hold the third polariser between them at 45 degrees to the first and observe that some light now gets through.
What you should see
The graph of I / I_max against cos² θ is a straight line close to slope 1. At 90 degrees the light nearly vanishes, but returns when a third filter at 45 degrees is inserted between the two.
Viva questions
A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.
01State Malus’s law.
I = I0 cos² θ, where θ is the angle between the transmission axes of polariser and analyser.
02What does polarisation show about light?
That light is a transverse wave.
03Why does a third filter let light through crossed filters?
The middle filter turns the plane of polarisation, so each pair of filters now has an angle less than 90 degrees.
04Where is polarised light used in daily life?
In sunglasses to cut glare, LCD screens and 3D cinema.
Take it further
Look through one filter at the sky at different angles from the Sun and note where the polarisation is strongest, at 90 degrees from the Sun.
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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