Q.37 Physics ⭐ 360° Option Elimination Active

NEET 2023 Physics Question 37 Solution

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

Question

In the figure shown here, what is the equivalent focal length of the combination of lenses (Assume that all layers are thin)?

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Verified Against NTA Final Answer Key

Option (4) : -100 cm

📚 Ray Optics and Optical Instruments Medium

📋 Given Parameters & Problem Setup

Central convex lens index (n₁) 1.5

Radii of curvature of central lens R₁ = 20 cm, R₂ = 20 cm

Surrounding medium index (n₂) 1.6

Shape of surrounding layers Two plano-concave liquid lenses with R = 20 cm

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The 30-Second Exam Hall Shortcut: ⚡ Power Addition Rule: 1/F = 1/f₁ + 1/f₂ + 1/f₃

⏱️ Save ~60 seconds

Central lens: 1/f₂ = (1.5-1)(1/20 + 1/20) = +1/20 = +5/100. Each liquid lens: 1/f = (1.6-1)(0 - 1/20) = -3/100. Total power 1/F = -3/100 + 5/100 - 3/100 = -1/100 ⟹ F = -100 cm in 30 seconds!

1 Decompose the system into three thin lenses in contact: two identical plano-concave liquid lenses (n₂ = 1.6) and one equiconvex lens (n₁ = 1.5).

2 For equiconvex glass lens: 1/f₂ = (n₁ - 1)(1/R₁ - 1/R₂) = (1.5 - 1)(1/20 - (-1/20)) = 0.5 × (2/20) = +1/20 cm⁻¹ = +5/100 cm⁻¹.

3 For each plano-concave liquid lens: 1/f_liquid = (n₂ - 1)(1/∞ - 1/20) = 0.6 × (-1/20) = -0.6/20 = -3/100 cm⁻¹.

4 Net power of thin lenses in contact: 1/F = 1/f₁ + 1/f₂ + 1/f₃ = (-3/100) + (+5/100) + (-3/100) = -1/100 cm⁻¹.

5 Equivalent focal length: F = -100 cm.

6 Lock Option (4) -100 cm with total conviction!

🛡️

Why You Can 100% Trust This Shortcut: Ray Optics · Lens Maker’s Formula (The equivalent optical power of thin coaxial lenses in contact is the algebraic sum of their individual powers: 1/F = Σ 1/f_i).

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Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Decomposition of the Composite Optical System

The given optical system consists of three thin lenses placed in contact along a common optical axis: (i) a first plano-concave lens made of the medium of refractive index n₂ = 1.6, (ii) an equiconvex lens made of material of refractive index n₁ = 1.5, and (iii) a second plano-concave lens made of the medium of refractive index n₂ = 1.6.

\frac{1}{F_{\text{eq}}} = \frac{1}{f_1} + \frac{1}{f_2} + \frac{1}{f_3}

Step 2

Focal Length of the Central Convex Lens (f₂)

Using the Lens Maker’s Formula for the central equiconvex lens in air with R₁ = +20 cm and R₂ = -20 cm:

\frac{1}{f_2} = (n_1 - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right) = (1.5 - 1)\left(\frac{1}{20} - \left(-\frac{1}{20}\right)\right) = 0.5 \times \frac{2}{20} = +\frac{1}{20}\text{ cm}^{-1} = +\frac{5}{100}\text{ cm}^{-1}

Step 3

Focal Length of the Left and Right Plano-Concave Lenses (f₁, f₃)

For the left plano-concave lens, the first surface is plane (R = ∞) and the second surface has radius of curvature R = +20 cm:

\frac{1}{f_1} = (n_2 - 1)\left(\frac{1}{\infty} - \frac{1}{20}\right) = (1.6 - 1)\left(-\frac{1}{20}\right) = -\frac{0.6}{20} = -\frac{3}{100}\text{ cm}^{-1}

Step 4

Summation of Individual Lens Powers

Because the right plano-concave lens is identical in curvature and material, 1/f₃ = -3/100 cm⁻¹. Summing all three powers:

\frac{1}{F} = \left(-\frac{3}{100}\right) + \left(+\frac{5}{100}\right) + \left(-\frac{3}{100}\right) = \frac{-3 + 5 - 3}{100} = -\frac{1}{100}\text{ cm}^{-1}

Step 5

Determination of Equivalent Focal Length

Inverting yields the net focal length of the combination:

F = -100\text{ cm}

⭐

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)

✗ Incorrect

Verdict & Scientific Reason:

Corresponds to omitting one of the two plano-concave liquid lenses (-3/100 + 5/100 = +2/100 ⟹ +50 cm).

⚠️

Student Fallacy (Why candidates pick this trap): Candidate forgot the second liquid layer.

2 (2)

✗ Incorrect

Verdict & Scientific Reason:

Incorrect sign and magnitude.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate treated the liquid lenses as convex instead of concave.

3 (3)

✗ Incorrect

Verdict & Scientific Reason:

Arithmetic slip in sign or curvature substitution.

⚠️

Student Fallacy (Why candidates pick this trap): Candidate made an error combining powers.

4 (4)

✓ 100% Correct

Verdict & Scientific Reason:

Accurate equivalent focal length matching Lens Maker’s Formula and NTA final answer key.

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Why this is airtight: None. Candidate correctly analyzed all three thin lens elements.

⚠️

NTA Trap Alert: Forgetting That Liquid Fills Both Sides (Two Concave Lenses)

The figure shows liquid on BOTH sides of the central lens, forming TWO plano-concave lenses. Candidates who treat the liquid as only one lens arrive at +50 cm or -50 cm.

🛡️ How to avoid the -1 mark: Count every boundary: Flat left + curved central + flat right = 3 distinct lens regions.

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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:

"Net focal length of thin lenses in contact satisfies 1/F = Σ (n_i - 1)(1/R₁ - 1/R₂)."

Syllabus Focus: Combination of Thin Lenses and Lens Maker’s Formula

Preserved in Rationalized Curriculum Syllabus & Academic Standards ↗

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NEET 2023 Physics Question 37 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Power Addition Rule: 1/F = 1/f₁ + 1/f₂ + 1/f₃

Step-by-Step Rigorous Workflow & Mathematical Proof

Decomposition of the Composite Optical System

Focal Length of the Central Convex Lens (f₂)

Focal Length of the Left and Right Plano-Concave Lenses (f₁, f₃)

Summation of Individual Lens Powers

Determination of Equivalent Focal Length

360° Option Elimination Engine Key Feature

NTA Trap Alert: Forgetting That Liquid Fills Both Sides (Two Concave Lenses)

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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