Q.11 Physics ⭐ 360° Option Elimination Active

NEET 2021 Physics Question 11 Solution

Topic: Ray Optics and Optical Instruments · Official NTA Booklet Code M1

Question

A convex lens 'A' of focal length 20 cm and a concave lens 'B' of focal length 5 cm are kept along the same axis with a distance 'd' between them. If a parallel beam of light falling on 'A' leaves 'B' as a parallel beam, then the distance 'd' in cm will be:

✓

Verified Against NTA Final Answer Key

Option (2) : 15

📚 Ray Optics and Optical Instruments Easy

📋 Given Parameters & Problem Setup

Convex Lens A Focal Length f_A = +20 cm

Concave Lens B Focal Length f_B = -5 cm

Condition Parallel incident beam emerges as a parallel beam (afocal system)

⚡

The 30-Second Exam Hall Shortcut: ⚡ Galilean Afocal Condition: d = f1 - |f2|

⏱️ Save ~20 seconds

When parallel light enters and leaves as parallel light, the focal points of both lenses must coincide! For a convex ( $f_1 = 20\text{ cm}$ ) and concave ( $|f_2| = 5\text{ cm}$ ) lens, distance $d = f_1 - |f_2| = 20 - 5 = 15\text{ cm}$ ! Match Option (2)!

1 Parallel beam on lens A converges towards its focus at distance

f_A = 20\text{ cm}

to the right.

2 For lens B to produce a parallel emergent beam, the virtual object must lie at the virtual focal point of lens B (

f_B = 5\text{ cm}

3 Thus, lens B must be placed

5\text{ cm}

before the focus of lens A.

4 Distance between lenses:

d = f_A - f_B = 20\text{ cm} - 5\text{ cm} = 15\text{ cm}

5 Match Option (2).

🛡️

Why You Can 100% Trust This Shortcut: Canonical Galilean telescope afocal ray optics geometry.

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Action of the First Convex Lens (Lens A)

A parallel beam of light falling on convex lens A has object distance $u_1 = \infty$ . By the lens formula, the image is formed at its principal focus:

v_1 = f_A = +20\text{ cm}

Step 2

Action of the Second Concave Lens (Lens B)

This real converging image acts as a virtual object for concave lens B placed at distance $d$ from A. The object distance for lens B is $u_2 = +(20 - d)$ . For the emergent beam to be parallel, the final image must be formed at infinity ( $v_2 = \infty$ ):

\frac{1}{v_2} - \frac{1}{u_2} = \frac{1}{f_B} \implies \frac{1}{\infty} - \frac{1}{u_2} = \frac{1}{-5} \implies u_2 = +5\text{ cm}

Step 3

Solving for the Separation Distance d

Equating $u_2 = 20 - d$ to $5\text{ cm}$ :

20 - d = 5 \implies d = 20 - 5 = 15\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:

Result of adding the focal lengths ( $20 + 5 = 25\text{ cm}$ ), which would be the condition if BOTH lenses were convex (Keplerian telescope).

⚠️

Student Fallacy (Why candidates pick this trap): Treating the concave lens as convex and calculating

f_1 + f_2

2 2

✓ 100% Correct

Verdict & Scientific Reason:

Exact separation distance for an afocal convex-concave combination: $d = f_A - |f_B| = 15\text{ cm}$ .

💡

Why this is airtight: None; rigorous geometric ray tracing.

3 3

✗ Incorrect

Verdict & Scientific Reason:

Arbitrary number with no optical basis.

⚠️

Student Fallacy (Why candidates pick this trap): Random guessing.

4 4

✗ Incorrect

Verdict & Scientific Reason:

Incorrect focal length combinations.

⚠️

Student Fallacy (Why candidates pick this trap): Calculation error.

⚠️

NTA Trap Alert: Convex-Convex vs. Convex-Concave Separation Trap

For two convex lenses (Keplerian telescope), the distance for an afocal system is $d = f_1 + f_2 = 25\text{ cm}$ . For a convex-concave pair (Galilean telescope), the distance is $d = f_1 - f_2 = 15\text{ cm}$ .

🛡️ How to avoid the -1 mark: Notice that lens B is CONCAVE (negative focal length), so subtract:

d = 20 - 5 = 15\text{ cm}

📖

Core NEET Syllabus Standard

NCERT Physics · Ray Optics and Optical Instruments Standard Benchmark

Core Scientific Principle Tested:

"In an afocal lens combination with parallel input and output beams, the second focal point of the first lens must coincide with the first focal point of the second lens ( $d = f_1 + f_2$ )."

Syllabus Focus: Combination of Thin Lenses in Contact and Separation

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2021 Physics Question 11 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ Galilean Afocal Condition: d = f1 - |f2|

Step-by-Step Rigorous Workflow & Mathematical Proof

Action of the First Convex Lens (Lens A)

Action of the Second Concave Lens (Lens B)

Solving for the Separation Distance d

360° Option Elimination Engine Key Feature

NTA Trap Alert: Convex-Convex vs. Convex-Concave Separation Trap

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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