Q.46 Physics ⭐ 360° Option Elimination Active

NEET 2023 Physics Question 46 Solution

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

Question

Two thin lenses are of same focal lengths (f), but one is convex and the other one is concave. When they are placed in contact with each other, the equivalent focal length of the combination will be:

✓

Verified Against NTA Final Answer Key

Option (1) : Infinite

📚 Ray Optics and Optical Instruments Easy

📋 Given Parameters & Problem Setup

Convex lens focal length (f₁) +f

Concave lens focal length (f₂) -f

Combination type Thin lenses in coaxial contact

⚡

The 30-Second Exam Hall Shortcut: ⚡ Power Cancellation: 1/F = 1/f - 1/f = 0 ⟹ F = ∞

⏱️ Save ~30 seconds

A convex lens (+f) and concave lens (-f) have equal and opposite powers: P_eq = +P - P = 0 ⟹ F = 1/0 = ∞ (Infinite / Glass Slab Behavior) in 5 seconds!

1 Equivalent focal length of thin lenses in contact: 1/F = 1/f₁ + 1/f₂.

2 For convex lens: f₁ = +f.

3 For concave lens: f₂ = -f.

4 Sum powers: 1/F = (1/f) + (-1/f) = 0.

5 Inverting gives focal length: F = 1 / 0 = ∞ (Infinite).

6 Lock Option (1) Infinite directly!

🛡️

Why You Can 100% Trust This Shortcut: Geometric Optics · Lens Power Combination (The equivalent optical power of thin lenses in contact is the algebraic sum of individual powers: P = P₁ + P₂).

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Governing Formula for Thin Lenses in Contact

When two thin lenses of focal lengths f₁ and f₂ are placed coaxially in direct physical contact, their powers add algebraically:

P = P_1 + P_2 \implies \frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2}

Step 2

Sign Convention for Converging and Diverging Elements

By optical sign convention, a convex (converging) lens has a positive focal length, while a concave (diverging) lens of identical magnitude has a negative focal length:

f_1 = +f, \qquad f_2 = -f

Step 3

Calculation of Equivalent Power and Focal Length

Substitute the focal lengths into the power equation:

\frac{1}{F} = \frac{1}{+f} + \frac{1}{-f} = \frac{1}{f} - \frac{1}{f} = 0

Step 4

Physical Meaning of Infinite Focal Length

Taking the reciprocal of zero power yields:

F = \frac{1}{0} = \infty \quad (\text{Infinite})

⭐

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:

Accurate: Zero net optical power corresponds to infinite focal length (acts like a plane glass plate).

💡

Why this is airtight: None. Candidate correctly summed powers.

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

Zero is the net POWER, not the net focal length.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate confused zero optical power (P = 0) with zero focal length (F = 0).

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

Arbitrary fractional option.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate misapplied parallel resistance formulas with wrong signs.

4 (4)

✗ Incorrect

Verdict & Scientific Reason:

Represents two CONVEX lenses of focal length f in contact (+f/2).

⚠️

Student Fallacy (Why candidates pick this trap): Candidate treated both lenses as convex (+f).

⚠️

NTA Trap Alert: Confusing Zero Power with Zero Focal Length

The net optical power is P = 0 D (the combination neither converges nor diverges parallel rays). But focal length is the reciprocal of power: F = 1/P = 1/0 = ∞. Choosing Zero (Option 2) is a frequent confusion between Power and Focal Length.

🛡️ How to avoid the -1 mark: Remember: A flat window glass pane has Power = 0 and Focal Length = ∞. The combination behaves as a flat glass slab!

📖

Core NEET Syllabus Standard

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

Core Scientific Principle Tested:

"Net focal length satisfies 1/F = 1/f₁ + 1/f₂. Equal opposite powers give 1/F = 0 ⟹ F = ∞."

Syllabus Focus: Combination of Thin Lenses in Contact

Preserved in Rationalized Curriculum Syllabus & Academic Standards ↗

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NEET 2023 Physics Question 46 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Power Cancellation: 1/F = 1/f - 1/f = 0 ⟹ F = ∞

Step-by-Step Rigorous Workflow & Mathematical Proof

Governing Formula for Thin Lenses in Contact

Sign Convention for Converging and Diverging Elements

Calculation of Equivalent Power and Focal Length

Physical Meaning of Infinite Focal Length

360° Option Elimination Engine Key Feature

NTA Trap Alert: Confusing Zero Power with Zero Focal Length

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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