Polarization Brewster

8 MCQs5 revision cards9-step worked example
Source: NCERT OpticsPYQ coverage: NEET 2020, 2024, 2025Official key: NTA-verifiedLast updated: 27 Sep 2026

Polarization Brewster, explained for NEET

The Brewster angle question is lost more often to the wrong trig function than to the arithmetic. Students write sin(i_B) = n, get an impossible value for n > 1, and either force it or pick the distractor built from sin⁻¹(1/n) — which is the critical angle, a different quantity from a different topic. Brewster's law is tan(i_B) = n. For glass with n = 1.50, i_B ≈ 56.3°; the critical angle for the same glass is ≈ 41.8°. They are never equal, and the examiner routinely offers both.

Why polarization at all: light is a transverse wave, so its electric field vibrates perpendicular to the direction of travel — and that vibration can be restricted to a single plane. Sunlight is unpolarized, containing every such orientation at random. When unpolarized light strikes a plane dielectric surface, the reflected and refracted beams are both partially polarized; at one particular angle of incidence the reflected beam becomes completely plane-polarized, with its vibration perpendicular to the plane of incidence. That angle is the Brewster angle, and this is the law NCERT Class 12 Physics (pre-2023 edition), Chapter 10, states on pages 380–381.

The geometric consequence worth memorising: at i_B, the reflected and refracted rays are perpendicular to each other. This follows directly — since tan(i_B) = n and Snell gives n = sin(i_B)/sin(r), you get r = 90° − i_B. That 90° separation is itself an examinable fact, and it also gives you a way to recover the angle when a question supplies the refracted ray instead of n.

Two conditions bound the law: the light must go from rarer to denser medium across a plane interface, and n is the index of the reflecting medium relative to the incident one. If n is quoted for a medium pair rather than relative to air, substitute the ratio, not the absolute value.

Watch-out: at Brewster's angle only the reflected beam is fully polarized. The refracted beam remains partially polarized — never completely.

Can you answer these Polarization Brewster 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

At Brewster's angle of incidence on a plane dielectric surface, the reflected light is

Show answer and why every option is right or wrong

Answer: A. A is correct. Brewster's angle is defined as the angle of incidence at which the reflected beam becomes completely plane-polarized, as stated in NCERT Class 12 Physics (pre-2023 edition), Chapter 10, pages 380–381.

Why B is wrong: B is wrong because partial polarization describes the reflected beam at a general angle of incidence, and also the refracted beam at Brewster's angle — but not the reflected beam at i_B itself.

Why C is wrong: C is wrong because the reflected beam at any angle of incidence on a dielectric carries at least partial polarization; at Brewster's angle it is fully polarized, never unpolarized.

Why D is wrong: D is wrong because reflection at a dielectric interface produces linear (plane) polarization, not circular; circular polarization requires a phase retardation the law does not involve.

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MCQ 2Easy RecallPractice

Brewster's law relates the polarizing angle i_B to the refractive index n of the reflecting medium as

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Answer: D. D is correct. Brewster's law is tan(i_B) = n, given in NCERT Class 12 Physics (pre-2023 edition), Chapter 10, pages 380–381.

Why A is wrong: A is wrong because sin(i_B) = n is the classic Brewster-for-Snell substitution error; for any n > 1 it demands sin(i_B) > 1, which has no solution.

Why B is wrong: B is wrong because sin(θ) = 1/n is the critical-angle condition for total internal reflection, a different phenomenon requiring denser-to-rarer incidence.

Why C is wrong: C is wrong because no cosine form appears in the law; this option tests whether the trig function was memorized or guessed.

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MCQ 3Easy RecallPractice

At Brewster's angle of incidence, the angle between the reflected ray and the refracted ray is

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Answer: B. B is correct. At i_B the reflected and refracted rays are mutually perpendicular — a direct geometric consequence of tan(i_B) = n combined with Snell's law, noted in NCERT Class 12 Physics (pre-2023 edition), Chapter 10, pages 380–381.

Why A is wrong: A is wrong because 45° has no standing in the law; the perpendicular relation is exact and independent of n.

Why C is wrong: C is wrong because 180° would place the refracted ray back along the reflected direction, contradicting the geometry of refraction into the denser medium.

Why D is wrong: D is wrong because a 0° separation would mean reflected and refracted rays travel together, which cannot happen at a refracting interface.

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MCQ 4Direct ApplicationPractice

Light travelling in a liquid of refractive index 1.20 strikes the plane surface of a denser transparent medium of refractive index 1.44. Using the refractive index of the second medium relative to the first, the Brewster angle for this interface is (Take tan 50.2° = 1.20)

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Answer: B. B is correct. Brewster's law uses the refractive index of the reflecting medium relative to the medium of incidence: n = n₂/n₁ = 1.44/1.20 = 1.20. Then i_B = tan⁻¹(1.20) = 50.2°. (Brewster's law, tan i_B = n: NCERT Class 12 Physics (pre-2023 edition), Chapter 10, page 381.)

Why A is wrong: A gives 39.8° — this inverts the ratio, using n₁/n₂ = 1.20/1.44 = 0.833 instead of n₂/n₁: tan⁻¹(0.833) = 39.8°. Brewster's law needs the index of the medium the light is entering relative to the medium it is leaving, not the reverse.

Why C is wrong: C gives 55.3° — this uses the second medium's index 1.44 directly, as if the light were travelling in air, ignoring that the incident medium already has index 1.20: tan⁻¹(1.44) = 55.3°.

Why D is wrong: D gives 56.4° — this confuses Brewster's law with the critical-angle relation sin(θ_c) = 1/n, applied to the relative index: sin⁻¹(1/1.20) = sin⁻¹(0.833) = 56.4°. Brewster's angle uses the tangent, not the sine, of the ratio.

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MCQ 5Direct ApplicationPractice

Light travelling in air is incident on a transparent medium of refractive index √3. The Brewster angle for this surface is

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Answer: D. D is correct. tan(i_B) = n = √3, so i_B = tan⁻¹(√3) = 60°. Brewster's law as stated in NCERT Class 12 Physics (pre-2023 edition), Chapter 10, pages 380–381.

Why A is wrong: A is wrong because 30° is tan⁻¹(1/√3) — the reciprocal has been taken, or the angle has been measured from the surface rather than from the normal.

Why B is wrong: B is wrong because 35.3° = sin⁻¹(1/√3), the critical angle for this medium — the standard sin-versus-tan substitution error.

Why C is wrong: C is wrong because 45° would require n = 1, i.e. no interface at all; it is the value obtained if the refractive index is ignored entirely.

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MCQ 6Direct ApplicationPractice

The polarizing angle for a certain glass surface in air is 57.0°. Taking tan 57.0° = 1.54, the refractive index of the glass is closest to

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Answer: C. C is correct. Brewster's law reads directly: n = tan(i_B) = tan 57.0° = 1.54. No inversion is needed. NCERT Class 12 Physics (pre-2023 edition), Chapter 10, pages 380–381.

Why A is wrong: A is wrong because 0.84 = sin 57.0°, obtained by using sin(i_B) = n instead of tan(i_B) = n.

Why B is wrong: B is wrong because 0.65 = 1/1.54, the result of inverting the correct answer as though the law were tan(i_B) = 1/n.

Why D is wrong: D is wrong because 1.19 = 1/sin 57.0°, the refractive index that would make 57.0° the critical angle — a sin-for-tan substitution in the wrong law.

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MCQ 7CalculationPractice

Unpolarized light in air strikes a plane surface at the Brewster angle, and the refracted ray inside the medium makes an angle of 33.0° with the normal. The refractive index of the medium is closest to (take tan 57.0° = 1.54)

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Answer: C. C is correct. At i_B the reflected and refracted rays are perpendicular, so i_B = 90° − 33.0° = 57.0°, giving n = tan 57.0° = 1.54. NCERT Class 12 Physics (pre-2023 edition), Chapter 10, pages 380–381.

Why A is wrong: A is wrong because 1.84 is 1/sin 33.0°: it treats the light as if it arrived at 90°, n = sin 90°/sin 33.0°. At the Brewster angle the reflected and refracted rays are perpendicular, so i_B = 90.0° − 33.0° = 57.0° and n = tan 57.0° = 1.54.

Why B is wrong: B is wrong because 0.65 is 1/1.54 — the reciprocal of the correct index, from inverting Brewster's law after finding the right angle.

Why D is wrong: D is wrong because 0.55 = sin 33.0°, which uses the refracted angle directly in a sine relation and skips the perpendicular-ray step entirely.

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MCQ 8CalculationPractice

For a certain transparent medium in air, the Brewster angle is i_B and the critical angle for total internal reflection at the same surface is θ_c. A student claims i_B = θ_c for every medium. This claim is

Show answer and why every option is right or wrong

Answer: A. A is correct. Both angles depend on n, but through different relations: tan(i_B) = n and sin(θ_c) = 1/n. Setting them equal gives sin²x = cos x, i.e. cos²x + cos x − 1 = 0, so cos x = 0.618 and x ≈ 51.8° at n ≈ 1.27 — one medium, not every medium. For n = 1.50 they are 56.3° and 41.8°. NCERT Class 12 Physics (pre-2023 edition), Chapter 10, pages 380–381.

Why B is wrong: B is wrong because equality occurs at one particular value of n, about 1.27, not throughout a range — and least of all above n = 2, where i_B is far the larger of the two.

Why C is wrong: C is wrong because sharing a dependence on n does not make two quantities equal; the functional forms differ, and so do the numerical values.

Why D is wrong: D is wrong in its direction: θ_c exceeds i_B only while n < 1.27 (at n = 1.1, 65.4° against 47.7°), and above that the order reverses (at n = 1.5, 41.8° against 56.3°). The verdict is right but the stated reason is not.

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Polarization Brewster: quick recall before you leave

How do you solve a Polarization Brewster question? A worked example

Pattern: Brewster's law calculation — find the polarizing angle from a given refractive index (the highest-relevance topic-specific PYQ pattern, seen in 2020, 2024 and 2025 papers).

  1. 1

    Given

    A beam of unpolarized light in air is incident on the plane surface of a liquid of refractive index n = 1.33 (exact, as quoted). Take tan 53.1° = 1.33.

  2. 2

    Required

    (a) The angle of incidence at which the reflected light is completely plane-polarized. (b) The angle of refraction at that incidence.

  3. 3

    Concept

    When unpolarized light meets a plane dielectric boundary, the reflected beam is in general partially polarized. At one specific angle of incidence — Brewster's angle — the reflected beam is completely plane-polarized, vibrating perpendicular to the plane of incidence. At that same angle the reflected and refracted rays are mutually perpendicular.

  4. 4

    Formula

    tan(i_B) = n, and consequently r = 90° − i_B.

  5. 5

    Substitution

    tan(i_B) = 1.33.

  6. 6

    Calculation

    i_B = tan⁻¹(1.33) = 53.1°. Then r = 90° − 53.1° = 36.9°. Note on significant figures: the 90° in the perpendicularity relation is an exact geometric value and the reflected-refracted perpendicularity is exact, so neither limits the precision — the three significant figures in the answers come from the given n = 1.33 alone.

  7. 7

    Final answer

    (a) i_B = 53.1°. (b) r = 36.9°.

  8. 8

    Common trap

    The dominant error is substituting into sin(i_B) = n. With n = 1.33 that demands sin(i_B) = 1.33, which is impossible — yet students who notice the impossibility often "fix" it by computing sin⁻¹(1/1.33) = 48.8° and selecting that. But 48.8° is the critical angle for this liquid, describing total internal reflection for light going the other way (denser to rarer). It is not the polarizing angle. Check the function before you check the arithmetic: Brewster uses tangent.

  9. 9

    Similar NEET-style question

    Unpolarized light in air falls on the flat surface of a transparent slab. It is found that the completely plane-polarized reflected beam makes an angle of 1.20 × 10² degrees with the incident beam. Find the refractive index of the slab. *(Hint: the angle between incident and reflected beams is 2i_B; solve for i_B first, then apply the law.)*

What to remember before solving Polarization Brewster questions

Law

Brewster's law

In the NEET syllabus; removed from current NCERT.

When unpolarised light is incident on the boundary between two transparent media and the reflected and refracted rays make a right angle with each other, the reflected light is totally polarised, with its electric vector perpendicular to the plane of incidence. This angle of incidence is Brewster's angle i_B, and tan i_B = mu, the refractive index (Eq. 10.36): Brewster's law. For an air-glass interface, mu = 1.5 gives i_B = 57 degrees (Example 10.9). At other angles the reflected light is partially polarised.

-- NCERT Class 12 Physics (pre-2023 edition), Chapter 10, p. 381

Which Polarization Brewster formulas do you need for NEET?

1 formula — click to collapse

Brewster's law

When light is incident at Brewster's angle on a dielectric, the reflected light is fully plane-polarised.

SymbolQuantitySI Unit
i_BBrewster's anglerad
nrefractive index-

Valid when

  • Light from rarer to denser medium (plane interface)
  • Linearly polarised reflected component perpendicular to plane of incidence

Where do students lose marks on Polarization Brewster?

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
Mistake

Uses sin(i_B) = n instead of tan(i_B) = n.

Root cause: formula misuse

Correction

Brewster's law: tan(i_B) = n (NOT sin). Different from Snell's critical angle sin(θ_c) = 1/n. Brewster ~57° for glass (n≈1.5); critical ~42°.

More in Optics: 8 exam traps and mistakes · 10 formulas · 6 question patterns from its other lessons.

Polarization Brewster questions from past NEET papers

3 questions from NEET 2020, 2024, 2025. Answers verified against NTA official keys. — click to collapse
NEET 2025

An unpolarized light beam travelling in air is incident on a medium of refractive index 1.73 at Brewster’s angle. Then

1Transmitted light is completely polarized with angle of refraction close to 30°
2Reflected light is completely polarized and the angle of reflection is close to 60°
3Reflected light is partially polarized and the angle of reflection is close to 30°
4Both reflected and transmitted light are perfectly polarized with angles of reflection and refraction close to 60° and 30°, respectively
NTA Answer: Option 2(final)

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All 21 past-paper questions from Optics →

How does NEET ask about Polarization Brewster?

1 recurring pattern from past papers — click to collapse

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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