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

⚡

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).

📐

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)

⭐

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.

📖

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 ↗

Ready to attempt under real exam pressure?

Test your speed and accuracy in the authentic 200-minute timed NTA simulator.

Launch NEET 2023 CBT Test →

← Previous (Q.30) All Physics Questions Grid Next (Q.32) →

Spotted a mistake in this solution? Report an error (support@mycompetitiveexams.com)

⚖️ Legal & Fair Dealing Notice: Sourced from publicly released NEET 2023 question papers and NEET answer keys for private study, research, and non-commercial educational practice under Fair Dealing (Section 52(1)(a) of the Indian Copyright Act, 1957). Not affiliated with or endorsed by NTA or NMC.

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?

🔗 Related Questions — Ray Optics and Optical Instruments

Apparent Depth Calculations Across Multi-Layer Dielectric Media

Two-Lens System Image Formation with Convex and Concave Lenses

Compound Microscope Magnification at Normal Adjustment

Combination of Lenses in Contact: Power and Magnification

Solve 4 NEET Questions a Day — One per Subject