Polarising filters in series and in use

6 minAS Level7.5.17.5.2

AI-drafted, independently checked · not yet teacher-reviewed

By the end of this lesson

By the end you can explain how a polarising filter works, calculate the intensity through several filters in series, and describe applications of polarisation.

Key to the symbols

The main symbols used in this lesson:

Symbol	Meaning
$I_2$	second (or new) intensity
$\theta_1$	first angle
$I_1$	first (or original) intensity

What is inside the filter?

A Polaroid filter contains long polymer molecules that have been stretched into parallel chains. The electrons in those chains can move easily along the chains, so the material absorbs light whose electric field oscillates along them.

The direction perpendicular to the chains is the transmission axis. Light oscillating along that axis passes through.

So the filter is not a set of physical slits. It is a material that absorbs one component of the electric field and transmits the other. The result is the same: the emerging light is plane-polarised along the transmission axis.

The first filter sets the plane of polarisation. Each later filter multiplies the intensity by

\cos^2\theta

for its own angle.

Crossed filters and the middle filter trick

Two filters with axes at $90^\circ$ are crossed. Light polarised by the first has no component along the second's axis, so nothing gets through.

Now slide a third filter between them, with its axis at $45^\circ$ to both. Something surprising happens: light comes out.

Here is why. The middle filter rotates the plane of polarisation. Light leaves it polarised at $45^\circ$ , not at $0^\circ$ . That $45^\circ$ beam has a component along the final filter's axis, so some light passes.

The middle filter does not add energy. It removes some light, but it also changes the direction of oscillation so that the final filter has something to transmit.

Worked example: Three filters at 0°, 45° and 90°

Plane-polarised light of intensity $100\ \text{W m}^{-2}$ passes through a filter at $45^\circ$ to its plane of polarisation, then through a second filter whose axis is $90^\circ$ to the original plane. Calculate the final intensity.

Have a go first?

Where polarisation shows up

Polarising sunglasses. Light reflected from a horizontal surface such as water or a road is partly polarised horizontally. Sunglasses with a vertical transmission axis absorb that component, cutting glare while letting through more of the useful vertical light.

Photography. A polarising filter on a camera can remove reflections from glass or water, so the camera sees through the surface instead of seeing the reflection.

LCD screens. A liquid-crystal display sits between two polarising filters. The liquid crystal rotates the plane of polarisation, and an applied voltage changes that rotation. Each pixel acts as a controllable shutter, so the screen can switch light on and off.

Stress analysis. Transparent plastic placed between crossed filters shows coloured patterns where it is stressed, because stress changes how it rotates polarisation. Engineers use this to find weak points in models.

Microwaves. A grid of parallel metal wires polarises microwaves: the component along the wires is absorbed or reflected, and the perpendicular component passes. Rotating the receiver shows the polarisation direction.

Common mistakes

A polarising filter blocks half the light by physically covering half the beam.

It transmits the component of the electric field along its axis and absorbs the perpendicular component. The beam is not cut in half geometrically; its oscillations are selected.

Crossed filters block all light, no matter what is between them.

A third filter at an intermediate angle rotates the plane of polarisation, so some light can pass through the final filter. Add the middle filter and the beam brightens from zero.

The middle filter increases the energy of the light.

Each filter can only reduce intensity. The middle filter changes the direction of polarisation, which allows the final filter to transmit some of what remains.

Polarising sunglasses work because they are darker than ordinary sunglasses.

In the exam

For a series, process the filters one at a time and recalculate the angle relative to the previous filter's axis.
Quote the intermediate intensities. "After the first filter, $I = 50\ \text{W m}^{-2}$ " shows the method even if the final arithmetic slips.
When explaining the three-filter result, say that the middle filter changes the plane of polarisation. That is the mark-winning idea.
Applications questions want the physics, not just the product: glare is partly polarised, the filter axis is chosen to absorb it.
Never claim a filter increases intensity. Each stage must reduce or keep it the same.

Key takeaways

A polarising filter transmits the component along its transmission axis and absorbs the perpendicular component.
Crossed filters transmit zero, but a filter at an intermediate angle between them allows some light through.
Each filter in series multiplies the intensity by $\cos^2\theta$ for its angle to the previous plane.
Sunglasses, cameras, LCDs, stress analysis and microwave grids all use polarisation.
Filters never increase intensity; they select and absorb.

Filters in series

CalculateQuestion 1 · Apply

Answer the 3 questions above to continue.