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CraftExam
medium difficulty10 min

Polarisation, Malus's Law and Brewster's Law

Polarisation is the restriction of light vibrations to one plane perpendicular to the direction of propagation. It proves that light waves are transverse.

In one line: Polariser selects a plane; analyser measures the cosine-squared component.

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Understand it

  • Ordinary light has electric-field vibrations in many planes perpendicular to the direction of travel.
  • A polariser transmits vibrations along its transmission axis and blocks the perpendicular component.
  • When polarised light passes through an analyser, the transmitted intensity depends on the angle between their transmission axes.
  • Reflection can also produce plane-polarised light at Brewster's angle.

Example

Polaroid sunglasses reduce glare from horizontal surfaces because reflected glare is strongly polarised and the lenses block much of that vibration direction.

Formula and rule

Malus's law assumptions: the incident light on the analyser is plane-polarised and the analyser is ideal.

Key step: resolve the electric-field amplitude along the analyser axis, E = E0 cos θ; since intensity is proportional to E2, the final result is I = I0 cos2 θ.

Brewster's law result: tan θB = n for incidence from air, with reflected and refracted rays perpendicular at θB.

Intensities are in W m−2 and refractive index has no SI unit.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

Plane-polarised light of intensity 80 W m−2 enters an analyser with its axis at 30 degree to the vibration direction.

  1. 1I = I0 cos2 θ = 80 x cos2 30 degree = 80 × 3/4 = 60 W m−2.
  2. 2The analyser transmits 60 W m−2.

Method you can reuse

  1. 1First identify whether the incident light is unpolarised or already plane-polarised.
  2. 2For unpolarised light, use I0/2 after the first polariser because only one vibration plane is selected.
  3. 3For plane-polarised light through an analyser, resolve the field component along the analyser axis and use I = I0 cos2 θ.
  4. 4For Brewster-angle questions, use tan θB = n and state the final geometry cue: reflected and refracted rays are at 90 degree to each other.

Visual tip

A diagram is useful when showing polariser and analyser axes, unpolarised light becoming plane-polarised light, and Brewster-angle reflection. Labels should include transmission axis, analyser angle θ, reflected ray, refracted ray and 90 degree angle between reflected and refracted rays at Brewster's angle.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

What is the transmitted intensity when plane-polarised light of intensity I0 passes through an analyser at 60 degree to its vibration direction?

Think first, then show answer
Using Malus's law, I = I0 cos2 60 degree = I0 × (1/2)2 = I0/4. So one-fourth of the incident plane-polarised intensity is transmitted.

Common wrong answer

A common wrong answer uses sin2 θ in Malus's law. The transmitted component is along the analyser axis, so the intensity varies as cos2 θ.

Don't mix this up

Students often apply Malus's law directly to unpolarised light without first halving the intensity after the first polariser. For unpolarised light through one ideal polariser, transmitted intensity becomes I0/2.

Exam tip

In Malus's law, θ is the angle between the transmission axes of the polariser and analyser, not the angle of incidence. For Brewster's law, tan θB = n is used for light incident from air into the medium.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

It is asked as proof of transverse nature, Malus's-law numerical, Brewster-angle calculation, or conceptual questions on glare reduction and crossed polaroids.
  1. 1

    Enough for 1 mark

    Polarisation is the restriction of light vibrations to one plane perpendicular to the direction of propagation. It proves that light waves are transverse.

  2. 2

    Add for 2 marks

    Example: Polaroid sunglasses reduce glare from horizontal surfaces because reflected glare is strongly polarised and the lenses block much of that vibration direction.

  3. 3

    Add for 3 marks

    Ordinary light has electric-field vibrations in many planes perpendicular to the direction of travel.

Practice

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