Q.43 Physics ⭐ 360° Option Elimination Active

NEET 2025 Physics Question 43 Solution

Topic: Wave Optics · Official NTA Booklet Code 45

Question

The intensity of transmitted light when a polaroid sheet, placed between two crossed polaroids at 22.5° from the polarization axis of one of the polaroid, is (I₀ is the intensity of polarised light after passing through the first polaroid):

✓

Verified Against NTA Final Answer Key

Option (3) : \frac{I_0}{8}

📚 Wave Optics Easy

📋 Given Parameters & Problem Setup

Initial Polarized Intensity I₀ (after passing through first polaroid P₁)

Configuration Two crossed polaroids (P₁ and P₃ at 90° to each other)

Intermediate Polaroid (P₂) Placed at 22.5° to the polarization axis of P₁

⚡

The 30-Second Exam Hall Shortcut: ⚡ Double Angle Malus Shortcut

⏱️ Save ~30 seconds

I = I₀ cos²(θ) cos²(90° - θ) = I₀ [cos θ sin θ]² = I₀ [sin(2θ) / 2]² = I₀ [sin(45°) / 2]² = I₀ [(1/√2) / 2]² = I₀ / 8!

1 Transmission through middle polaroid at θ = 22.5°: I₁' = I₀ cos²(22.5°).

2 Angle between middle and third (crossed) polaroid: 90° - 22.5° = 67.5°.

3 Transmission through third polaroid: I_final = I₁' cos²(67.5°) = I₀ cos²(22.5°) sin²(22.5°).

4 Use trigonometric identity: sin θ cos θ = sin(2θ) / 2.

5 Here 2θ = 2 × 22.5° = 45°. Since sin 45° = 1/√2, sin(2θ) / 2 = 1 / (2√2).

6 Square it: [1 / (2√2)]² = 1 / 8 ⟹ I_final = I₀ / 8.

7 Match Option (3) in under 15 seconds!

🛡️

Why You Can 100% Trust This Shortcut: Malus’s Law of Polarization (NCERT Physics · Wave Optics: I = I₀ cos²θ).

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Apply Malus’s Law to Second Polaroid P₂

The light emerging from the first polaroid P₁ has intensity I₀ and is linearly polarized along P₁’s transmission axis. When it strikes polaroid P₂ at an angle θ = 22.5°:

I_2 = I_0 \cos^2(22.5^\circ)

• The light transmitted through P₂ is now polarized along P₂’s axis.

Step 2

Apply Malus’s Law to Third Polaroid P₃

P₃ is crossed with P₁, meaning its transmission axis is at 90° to P₁. The angle between P₂ and P₃ is therefore 90° - 22.5° = 67.5°:

I_{final} = I_2 \cos^2(67.5^\circ) = I_0 \cos^2(22.5^\circ) \cos^2(67.5^\circ)

• Since cos(67.5°) = cos(90° - 22.5°) = sin(22.5°):
• I_{final} = I_0 [\cos(22.5^\circ) \sin(22.5^\circ)]^2.

Step 3

Simplify Using Double-Angle Trigonometric Identity

Using the identity 2 sin θ cos θ = sin(2θ):

I_{final} = I_0 \left[\frac{\sin(2 \times 22.5^\circ)}{2}\right]^2 = I_0 \left[\frac{\sin(45^\circ)}{2}\right]^2 = I_0 \left[\frac{1 / \sqrt{2}}{2}\right]^2 = I_0 \left[\frac{1}{2\sqrt{2}}\right]^2 = \frac{I_0}{8}

• Matches Option (3) exactly.

⭐

360° Option Elimination Engine Key Feature

Diagnose every choice: Know exactly why the right option works and why distractors fail.

4-Option Deep Scan

1 A

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Corresponds to unpolarized light passing through a single polaroid.

⚠️

Student Fallacy (Why candidates pick this trap): Applying half-intensity rule for unpolarized light.

2 B

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. This would be the result if the intermediate polaroid were oriented at 45° instead of 22.5°: (I₀/4) sin²(90°) = I₀ / 4.

⚠️

Student Fallacy (Why candidates pick this trap): Assuming θ = 45° standard textbook case.

3 C

✓ 100% Correct

Verdict & Scientific Reason:

100% correct. I = (I₀/4) sin²(45°) = (I₀/4) × (1/2) = I₀ / 8.

💡

Why this is airtight: None; rigorous Malus’s law application.

4 D

✗ Incorrect

Verdict & Scientific Reason:

Incorrect. Squaring an extra factor of 2.

⚠️

Student Fallacy (Why candidates pick this trap): Using (1/4)² instead of 1/8.

⚠️

NTA Trap Alert: Confusing 22.5° with the Classic 45° Case

The standard NCERT textbook example places the sheet at 45°, giving I₀ / 4 (Option 2). In this exam, NTA modified the angle to 22.5°, yielding I₀ / 8!

🛡️ How to avoid the -1 mark: Always check the given angle: at 45° it is I₀/4; at 22.5° it is I₀/8!

📖

Core NEET Syllabus Standard

NEET Physics Core Syllabus · Wave Optics Standard Benchmark

Core Scientific Principle Tested:

"Intensity through successive polarizers: I = I₀ cos²θ₁ cos²θ₂ = (I₀/4) sin²(2θ)."

Syllabus Focus: Polarization and Malus’s Law

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

Double the angle 22.5° ⟹ 45° ⟹ sin²(45°)/4 = (1/2)/4 = 1/8 ⟹ I₀ / 8!

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NEET 2025 Physics Question 43 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Double Angle Malus Shortcut

Step-by-Step Rigorous Workflow & Mathematical Proof

Apply Malus’s Law to Second Polaroid P₂

Apply Malus’s Law to Third Polaroid P₃

Simplify Using Double-Angle Trigonometric Identity

360° Option Elimination Engine Key Feature

NTA Trap Alert: Confusing 22.5° with the Classic 45° Case

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

🔗 Related Questions — Wave Optics

Young’s Double Slit Experiment with White Light

State of Polarization of Reflected and Refracted Light at Brewster’s Angle

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Brewster's Law and Range of Brewster's Polarizing Angle: 45° < ib < 90°

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