Q.31 Physics ⭐ 360° Option Elimination Active

NEET 2023 Physics Question 31 Solution

Topic: Ray Optics and Optical Instruments · Official NTA Booklet Code G5

Question

Light travels a distance x in time t₁ in air and 10x in time t₂ in another denser medium. What is the critical angle for this medium?

✓

Verified Against NTA Final Answer Key

Option (1) : sin⁻¹(10 t₁ / t₂)

📚 Ray Optics and Optical Instruments Easy

📋 Given Parameters & Problem Setup

Distance in air x in time t₁

Speed of light in air (v₁) x / t₁

Distance in denser medium 10x in time t₂

Speed of light in medium (v₂) 10x / t₂

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The 30-Second Exam Hall Shortcut: ⚡ Critical Angle & Speed Ratio: sin θ_c = 1 / μ = v_med / v_air

⏱️ Save ~45 seconds

v_air = x / t₁ and v_med = 10x / t₂. Critical angle sin θ_c = v_med / v_air = (10x / t₂) / (x / t₁) = 10 t₁ / t₂ ⟹ θ_c = sin⁻¹(10 t₁ / t₂) in 15 seconds!

1 Recall critical angle formula: sin θ_c = 1 / μ.

2 Refractive index μ = v_air / v_med ⟹ sin θ_c = v_med / v_air.

3 Speed in medium v_med = distance / time = 10x / t₂.

4 Speed in air v_air = distance / time = x / t₁.

5 Form the ratio: sin θ_c = (10x / t₂) / (x / t₁) = (10x / t₂) × (t₁ / x) = 10 t₁ / t₂.

6 Invert: θ_c = sin⁻¹(10 t₁ / t₂). Option (1) is instantly secured!

🛡️

Why You Can 100% Trust This Shortcut: Wave & Ray Optics · Snell’s Law and Critical Angle (sin θ_c = 1/μ = v_denser / v_rarer).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Definition of Critical Angle

When light travels from an optically denser medium of refractive index μ into an optically rarer medium (air, μ_air ≈ 1), total internal reflection occurs at the critical angle of incidence θ_c where the angle of refraction is 90°:

\sin \theta_c = \frac{1}{\mu}

Step 2

Refractive Index in Terms of Wave Speeds

By the wave definition of refractive index, μ is the ratio of the speed of light in air (v_1) to the speed of light in the denser medium (v_2):

\mu = \frac{v_1}{v_2} \implies \sin \theta_c = \frac{v_2}{v_1}

Step 3

Evaluation of Speeds from Given Distances and Times

Using the kinematic relation speed = distance / time for each medium:

v_1 = \frac{x}{t_1}, \qquad v_2 = \frac{10x}{t_2}

Step 4

Substitution and Derivation of Critical Angle

Substitute v_1 and v_2 into the critical angle relation:

\sin \theta_c = \frac{\frac{10x}{t_2}}{\frac{x}{t_1}} = \frac{10x}{t_2} \times \frac{t_1}{x} = \frac{10 t_1}{t_2} \implies \theta_c = \sin^{-1}\left(\frac{10 t_1}{t_2}\right)

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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 (1)

✓ 100% Correct

Verdict & Scientific Reason:

Exact derivation matching Snell’s Law and NTA final answer key.

💡

Why this is airtight: None. Candidate correctly linked v_med / v_air to sin θ_c.

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

Omitted the factor of 10.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate forgot the 10x distance in the second medium.

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

Inverted the time ratio (t₂ / t₁ instead of t₁ / t₂).

⚠️

Student Fallacy (Why candidates pick this trap): Candidate confused the numerator and denominator of the velocity ratio.

4 (4)

✗ Incorrect

Verdict & Scientific Reason:

Placed the factor 10 in the denominator instead of the numerator.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate inverted the distance factor.

⚠️

NTA Trap Alert: Inverting the Ratio (Thinking sin θ_c = μ)

Since sine cannot exceed 1, sin θ_c = 1 / μ = v_med / v_air. Candidates who accidentally compute μ = v_air / v_med get t₂ / (10 t₁), which is greater than 1 and physically impossible inside the arcsin function.

🛡️ How to avoid the -1 mark: Sanity check: Critical angle sine MUST be < 1. Since medium is denser, v_med < v_air, hence sin θ_c = v_med / v_air.

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Core NEET Syllabus Standard

National Eligibility cum Entrance Test (NEET UG) · Ray Optics and Optical Instruments Standard Benchmark

Core Scientific Principle Tested:

"The critical angle is given by sin θ_c = 1/μ = v_medium / v_air."

Syllabus Focus: Total Internal Reflection and Critical Angle

Preserved in Rationalized Curriculum Syllabus & Academic Standards ↗

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NEET 2023 Physics Question 31 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Critical Angle & Speed Ratio: sin θ_c = 1 / μ = v_med / v_air

Step-by-Step Rigorous Workflow & Mathematical Proof

Definition of Critical Angle

Refractive Index in Terms of Wave Speeds

Evaluation of Speeds from Given Distances and Times

Substitution and Derivation of Critical Angle

360° Option Elimination Engine Key Feature

NTA Trap Alert: Inverting the Ratio (Thinking sin θ_c = μ)

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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