Key Fact
Polaroid
Polarising film that transmits light only with electric vector along its axis. Two crossed polaroids block all light. Malus's law: I = I_0 cos²θ.
-- NCERT Class 12 Physics, Ch. 10, p. 271Polaroid
8 MCQs2 revision cards9-step worked example
Source: NCERT OpticsPYQ coverage: NEET 2025Official key: NTA-verifiedLast updated: 21 Sep 2026
Polaroid, explained for NEET
The square is where marks are lost. Malus's law is I = I₀cos²θ, and dropping the square turns θ = 60° from I₀/4 into I₀/2 — a value that sits in the options, waiting. Write cos²θ before you substitute anything.
A Polaroid is a sheet that transmits only the component of the electric field along its pass axis. NCERT Class 12 Physics Part 2, Chapter 10, page 272 states the two behaviours you need. First, when unpolarized light falls on a single Polaroid, the transmitted intensity is exactly half the incident intensity, whatever the orientation — rotate the sheet and nothing changes. Malus's law does not apply here, because unpolarized light has no single polarization direction; averaging cos²θ over all directions gives the factor ½.
Second, once light is plane-polarized, Malus's law governs everything downstream: I = I₀cos²θ, where θ is the angle between the incoming polarization direction and the pass axis of the next Polaroid.
That two-stage structure is the whole game in NEET. A polarizer–analyser stack question is read left to right: the first sheet halves the unpolarized beam and fixes its polarization along its own axis; every subsequent sheet applies cos² of the angle between consecutive axes, not the angle measured from the original beam. Crossed Polaroids (90° apart) transmit zero — and inserting a third sheet between them at an intermediate angle lets light through again, because each stage now sees a non-zero angle.
Uses follow from this. Polaroid sunglasses cut glare, which is largely horizontally polarized light reflected from roads and water; the lenses are mounted with a vertical pass axis. LCD displays, photographic filters that darken a blue sky, and stress analysis in transparent models all exploit the same selective transmission.
Watch-out: identify whether the light arriving at each sheet is unpolarized (use ½) or already polarized (use cos²θ). Applying the ½ factor twice, or applying cos²θ to the first sheet, are the two ways this goes wrong.
Can you answer these Polaroid MCQs?
Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.
MCQ 1Easy RecallPractice
A Polaroid sheet transmits light whose electric field vibrates
Show answer and why every option is right or wrong
Answer: C. A Polaroid passes the component of the electric field parallel to its pass axis and absorbs the perpendicular component, as described in NCERT Class 12 Physics Part 2, Chapter 10, page 272.
Why A is wrong: A is wrong because that describes unpolarized light arriving at the sheet, not light leaving it; the sheet's whole function is to select one direction.
Why B is wrong: B is wrong because the component perpendicular to the pass axis is the one that is absorbed, not transmitted.
Why D is wrong: D is wrong because light is a transverse wave — the electric field is always perpendicular to the direction of propagation, so no Polaroid could transmit a field along it.
MCQ 2Easy RecallPractice
Unpolarized light of intensity I₀ falls on a single ideal Polaroid. The transmitted intensity is
Show answer and why every option is right or wrong
Answer: B. Unpolarized light contains all vibration directions equally, and averaging cos²θ over all of them gives ½, so exactly half the intensity is transmitted whatever the orientation — stated in NCERT Class 12 Physics Part 2, Chapter 10, page 272.
Why A is wrong: A is wrong because the sheet absorbs the component perpendicular to its pass axis, so the beam must lose intensity.
Why C is wrong: C is wrong because Malus's law needs a single incoming polarization direction to measure θ from; unpolarized light has none, which is exactly why the result is the orientation-free factor ½.
Why D is wrong: D is wrong because a Polaroid has no preferred absolute orientation — nothing in the physics singles out the vertical for an unpolarized input.
MCQ 3Direct ApplicationPractice
Plane-polarized light of intensity I₀ is incident on a Polaroid whose pass axis makes 60° with the light's polarization direction. The transmitted intensity is
Show answer and why every option is right or wrong
Answer: B. Malus's law gives I = I₀cos²60° = I₀ × (0.5)² = I₀/4. The rule and this form appear in NCERT Class 12 Physics Part 2, Chapter 10, page 272.
Why A is wrong: A is wrong because it is I₀cos 60° — the square has been dropped, which is the single most common slip on this formula.
Why C is wrong: C is wrong because it uses sin 60° without squaring; both errors are present at once.
Why D is wrong: D is wrong because it is I₀sin²60°, measuring the angle from the wrong reference — θ in Malus's law is between the polarization direction and the pass axis, and here that angle is given directly as 60°.
MCQ 4Direct ApplicationPractice
Light emerging from a Polaroid is reduced to one-half of its intensity by a second Polaroid placed behind it. The angle between the two pass axes is
Show answer and why every option is right or wrong
Answer: C. Setting cos²θ = 1/2 gives cos θ = 1/√2, so θ = 45°. The light leaving the first Polaroid is already plane-polarized, so Malus's law applies directly — see NCERT Class 12 Physics Part 2, Chapter 10, page 272.
Why A is wrong: A is wrong because cos²30° = 3/4, so the second sheet would transmit three-quarters, not half.
Why B is wrong: B is wrong because cos²60° = 1/4 — this is the answer a student reaches by solving cos θ = 1/2 instead of cos²θ = 1/2.
Why D is wrong: D is wrong because crossed Polaroids transmit zero, which is the one case where the answer does not depend on getting the square right.
MCQ 5Concept TrapPractice
Two Polaroids are crossed, so no light emerges. A third Polaroid is now inserted between them with its pass axis at 45° to each. Light is observed emerging from the stack. The reason is that
Show answer and why every option is right or wrong
Answer: A. The middle Polaroid transmits the component along its own axis, so the light leaving it is polarized at 45° — no longer at 90° to the final sheet, which therefore passes cos²45° of it. This follows from applying the selective-transmission behaviour of NCERT Class 12 Physics Part 2, Chapter 10, page 272 stage by stage.
Why B is wrong: B is wrong because a Polaroid works by selective absorption along an axis, not by redirecting the beam around the next element.
Why C is wrong: C is wrong because it states a general rule that is false — adding a sheet at 0° or 90° to the existing pair changes nothing, and the effect here depends entirely on the intermediate angle.
Why D is wrong: D is wrong because a Polaroid can only remove a component; it cannot restore the randomness of unpolarized light. The emerging light is plane-polarized at 45°.
MCQ 6CalculationPractice
Unpolarized light of intensity I₀ passes through two Polaroids whose pass axes are 30° apart. The intensity emerging from the second Polaroid is
Show answer and why every option is right or wrong
Answer: A. The first sheet halves the unpolarized beam to I₀/2 and polarizes it along its own axis; the second then gives (I₀/2)cos²30° = (I₀/2)(3/4) = 3I₀/8. Both stages are read off NCERT Class 12 Physics Part 2, Chapter 10, page 272.
Why B is wrong: B is wrong because it applies Malus's law to the first sheet as well, skipping the ½ factor that unpolarized input demands.
Why C is wrong: C is wrong because it uses cos²60° at the second stage — the angle in Malus's law is between the two pass axes, which is 30°, not its complement.
Why D is wrong: D is wrong because the square on the cosine has been dropped after the ½ factor was correctly applied: (I₀/2)cos30° = I₀√3/4.
MCQ 7Concept TrapPractice
Polaroid sunglasses are effective against glare from a wet road because the reflected glare is largely
Show answer and why every option is right or wrong
Answer: C. Light reflected from a horizontal surface is predominantly polarized parallel to that surface, so mounting the pass axis vertically removes most of it — one of the standard uses of plane-polarized light listed in NCERT Class 12 Physics Part 2, Chapter 10, page 272.
Why A is wrong: A is wrong on both halves: the glare's usefulness as an example depends on it being partially polarized, and a Polaroid transmits half of any unpolarized light rather than blocking it.
Why B is wrong: B is wrong because it reverses both the glare's polarization and the lens axis; a horizontal pass axis would transmit road glare preferentially, making the lenses worse than plain glass.
Why D is wrong: D is wrong because light is transverse — there is no electric-field component along the direction of propagation to be polarized.
MCQ 8CalculationPractice
Plane-polarized light passes through a Polaroid, and the sheet is then rotated until the transmitted intensity falls to one-quarter of its maximum value. Through what angle, measured from the position of maximum transmission, has the sheet been rotated?
Show answer and why every option is right or wrong
Answer: D. Maximum transmission occurs at θ = 0, so I/I_max = cos²θ = 1/4 gives cos θ = 1/2 and θ = 60.0°. Malus's law in this ratio form follows directly from NCERT Class 12 Physics Part 2, Chapter 10, page 272.
Why A is wrong: A is wrong because it comes from solving cos²θ = 1/4 as though the quarter applied to the cosine before squaring in the other direction; cos 75° ≈ 0.26, giving roughly 0.07 of the maximum.
Why B is wrong: B is wrong because cos²30° = 3/4 — this is the angle at which three-quarters is transmitted, not one-quarter.
Why C is wrong: C is wrong because the maximum-transmission position is θ = 0, and a 15° rotation leaves cos²15° ≈ 0.93 of the intensity, almost unchanged.
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Polaroid: quick recall before you leave
How do you solve a Polaroid question? A worked example
Pattern: Malus's law applied to a polarizer–analyser stack.
- 1
Given
• Incident light: unpolarized, intensity I₀ = 8.0 × 10¹ W/m²• Angle between the pass axes of the two Polaroids: θ = 30° (exact)• Both Polaroids ideal
- 2
Required
The intensity transmitted through the second Polaroid.
- 3
Concept
Two distinct stages. The first Polaroid receives unpolarized light, so it transmits half the intensity and leaves the beam plane-polarized along its own pass axis. The second Polaroid receives plane-polarized light, so Malus's law applies, with θ measured between the two pass axes.
- 4
Formula
Stage 1: I₁ = I₀/2
Stage 2: I₂ = I₁cos²θ - 5
Substitution
I₁ = (8.0 × 10¹ W/m²)/2
I₂ = I₁ × cos²(30°) - 6
Calculation
I₁ = 4.0 × 10¹ W/m²
cos 30° = √3/2, so cos²30° = 3/4 = 0.75
I₂ = (4.0 × 10¹ W/m²) × 0.75 = 3.0 × 10¹ W/m²
The factor 2 in I₀/2, the angle 30°, and the value √3/2 are exact — a counting factor, an exact angle, and a mathematical constant respectively. None of them limits the significant figures. The precision comes only from I₀ = 8.0 × 10¹ W/m², which carries two significant figures. - 7
Final answer
I₂ = 3.0 × 10¹ W/m² (two significant figures)
- 8
Common trap
Dropping the square. Using cos 30° instead of cos²30° gives (4.0 × 10¹)(0.866) ≈ 3.5 × 10¹ W/m² — close enough to the correct value to look plausible, and reliably present in the options. The second trap is applying cos²θ at the first sheet too, which gives (8.0 × 10¹)(0.75) = 6.0 × 10¹ W/m². Decide at each sheet whether the arriving light is unpolarized (½) or polarized (cos²θ) before writing anything.
- 9
Similar NEET-style question
Unpolarized light of intensity 1.20 × 10² W/m² passes through three Polaroids. The second is at 45° to the first, and the third is at 45° to the second. What intensity emerges? (Apply ½ at the first sheet, then cos²45° twice, using the angle between consecutive axes each time.)
What to remember before solving Polaroid questions
Which Polaroid formulas do you need for NEET?
1 formula — click to collapse
Malus's law
Intensity through a polariser depends on angle theta between light's polarisation and polariser axis.
| Symbol | Quantity | SI Unit |
|---|---|---|
| I | transmitted intensity | W/m^2 |
| I0 | incident intensity | W/m^2 |
| theta | angle | rad |
Valid when
- Linearly polarised input
- Ideal polariser
Where do students lose marks on Polaroid?
These are the exact patterns that cause wrong answers in NEET. Each trap includes when it triggers and how to avoid it.
1 item — click to collapse
Root cause: formula misuse
Correction
Malus: I = I_0 cos²(θ). For θ=60°: I = I_0 × (1/4), not I_0 × 0.5.
More in Optics: 8 exam traps and mistakes · 10 formulas · 6 question patterns from its other lessons.
Polaroid questions from past NEET papers
1 question from NEET 2025. Answers verified against NTA official keys. — click to collapse
NEET 2025
1I₀/16
2I₀/2
3I₀/4
4I₀/8
NTA Answer: Option 4(final)
How does NEET ask about Polaroid?
1 recurring pattern from past papers — click to collapse
Malus's law I = I_0 cos²(θ). Find transmitted intensity through polariser stack.
Direct ApplicationEasy
Common distractors
uses cos not cos squared
Drops square on cos
Sources
Page numbers are the ones printed in the current NCERT textbook (2023 rationalised edition), unless marked pre-2023. The books are free at ncert.nic.in.
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