A Polaroid filter is made from a special material that selectively transmits one component of an electromagnetic wave. The electric-field component parallel to the filter's transmission axis passes through, while the perpendicular component is strongly absorbed.
Transmission axis
The direction in which the filter transmits the electric-field vibration is called its transmission axis or polarization axis. The electric field of the emerging plane-polarized light is parallel to this axis.
Polarizer
When a Polaroid is used to convert unpolarized light into plane-polarized light, it is called a polarizer. The random transverse electric-field directions are resolved along the filter axis, and only the parallel component is transmitted.
Intensity after the first Polaroid
For ideal unpolarized light, all transverse vibration directions are equally likely. Averaging the transmitted component over all directions gives one half of the incident intensity.
Key equation
Ip=Iu2
I_u
Intensity of incident unpolarized light (W m⁻²)
I_p
Intensity after the first ideal Polaroid (W m⁻²)
Analyzer
A second Polaroid placed after the polarizer is called an analyzer. Rotating the analyzer changes the angle between the two transmission axes and therefore changes the transmitted intensity.
Device
Function
Polarizer
Produces plane-polarized light from unpolarized light
Analyzer
Tests the polarization direction and controls transmitted intensity
Malus's law
If plane-polarized light of intensity I₀ falls on an analyzer and θ is the angle between the polarizer and analyzer transmission axes, the transmitted intensity is proportional to the square of the cosine of θ.
Key equation
I∝cos2θ
Key equation
I=I0cos2θ
I
Intensity transmitted by the analyzer (W m⁻²)
I_0
Intensity incident on the analyzer; already polarized (W m⁻²)
θ
Angle between the transmission axes (degree or radian)
Special orientations
Angle θ
Axis arrangement
Calculation
Ideal transmitted intensity
0°
Parallel
I=I0cos2 0°
I=I0
45°
Inclined
I=I0cos2 45°
I=I02
90°
Crossed
I=I0cos2 90°
I=0
Crossed Polaroids
When the analyzer axis is perpendicular to the polarizer axis, the analyzer blocks the vibration direction produced by the polarizer. Ideally no light is transmitted. This directional effect is explained by the transverse wave model of light.
Key equation
I=I0cos2(90°)=0
Worked example
Two Polaroids at 60°
Unpolarized light of intensity 80 W m⁻² passes through an ideal polarizer and then through an analyzer whose axis is 60° to the polarizer. Find the final intensity.
1
Given
Iu=80W m-2
θ=60°
2
Working
I0=Iu2=802=40W m-2
3
Step 2
I=I0cos2θ=40cos2(60°)
4
Step 3
I=40(12)2=10W m-2
Final answer: The final transmitted intensity is 10 W m⁻².
Common mistakes
Check your understanding
Q. What is the transmission axis of a Polaroid?
A. It is the direction of electric-field vibration that the filter transmits.
Q. What is the difference between a polarizer and an analyzer?
A. A polarizer produces plane-polarized light; an analyzer is a second filter used to examine its direction and intensity.
Q. What happens when two ideal Polaroids are crossed?
A. Their axes differ by 90°, so the analyzer transmits zero intensity ideally.
Q. What does I₀ represent in Malus's law?
A. It is the intensity of already polarized light incident on the analyzer.
Quick revision
A Polaroid transmits one electric-field vibration direction and absorbs the perpendicular component.
The allowed direction is called the transmission axis or polarization axis of the filter.
A Polaroid that produces polarized light is called a polarizer.
A second Polaroid used to examine polarized light is called an analyzer.
Ideal unpolarized light emerges from the first Polaroid with half its original intensity.
Malus's law is I=I₀cos²θ, where θ is the angle between polarizer and analyzer transmission axes.
Parallel axes give maximum transmitted intensity, while crossed axes at 90° ideally transmit no light.
The crossed-Polaroid result is wave evidence because it depends on the direction of transverse vibration.
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Exam preparation
Exam Focus
Important points
Transmission axis and filter action.
Polarizer versus analyzer.
First ideal Polaroid transmits half of unpolarized intensity.
Malus's law: I=I₀cos²θ.
Parallel and crossed axes.
Common mistakes
Using cos θ instead of cos²θ.
Forgetting the first Polaroid halves unpolarized intensity.
Measuring θ from the ray rather than between axes.
Confusing polarizer and analyzer roles.
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.
Polarization by a Polaroid Filter
Sticky Notes · Quick Revision
1.
Key Point 1
A Polaroid transmits one electric-field vibration direction and absorbs the perpendicular component.
2.
Key Point 2
A Polaroid that produces polarized light is called a polarizer.
3.
Key Point 3
Malus's law is I=I₀cos²θ, where θ is the angle between polarizer and analyzer transmission axes.
4.
Key Point 4
Parallel axes give maximum transmitted intensity, while crossed axes at 90° ideally transmit no light.
Ready to test yourself?
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8 concept questions
Easy → Medium → Hard
Explanation after each answer
Exam Practice
Important Question
Q1. Explain how a Polaroid filter produces plane-polarized light.
Important Question
Q2. Differentiate between a polarizer and an analyzer.
Important Question
Q3. State Malus's law and define its symbols.
Reasoning
Q4. Why do crossed ideal Polaroids transmit no light?
Numerical
Q5. Unpolarized light of intensity 80 W m⁻² passes through ideal Polaroids at 60°. Find the final intensity.
