Q.37 Physics ⭐ 360° Option Elimination Active

NEET 2021 Physics Question 37 Solution

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

Question

A point object is placed at a distance of 60 cm from a convex lens of focal length 30 cm. If a plane mirror were put perpendicular to the principal axis of the lens and at a distance of 40 cm from it, the final image would be formed at a distance of:

✓

Verified Against NTA Final Answer Key

Option (4) : 20 cm from the plane mirror, it would be a virtual image.

📚 Ray Optics and Optical Instruments Medium

📋 Given Parameters & Problem Setup

Object Distance from Lens (u) -60 cm

Focal Length of Convex Lens (f) +30 cm

Distance of Plane Mirror from Lens (d) 40 cm

⚡

The 30-Second Exam Hall Shortcut: ⚡ 2f Image + Plane Mirror Object Distance

⏱️ Save ~25 seconds

Object is at $2f = 60\text{ cm}$ , so lens would form real image at $v = 60\text{ cm}$ behind the lens. The mirror is placed at $40\text{ cm}$ , intercepting the rays $60 - 40 = 20\text{ cm}$ before focus. This point acts as a virtual object at $20\text{ cm}$ behind the mirror! The reflected image is formed at $20\text{ cm}$ from the plane mirror. Match Option (4)!

1 Lens equation:

u = -60\text{ cm}, f = +30\text{ cm} \implies v = +60\text{ cm}

(at

2f

2 Mirror position: Placed at

d = 40\text{ cm}

to the right of the lens.

3 Position of intermediate image relative to mirror:

60\text{ cm} - 40\text{ cm} = 20\text{ cm}

behind the mirror.

4 By plane mirror reflection: The image distance from mirror equals object distance

= 20\text{ cm}

from the plane mirror.

5 Official NTA key categorizes this as: 20 cm from the plane mirror, it would be a virtual image.

6 Match Option (4).

🛡️

Why You Can 100% Trust This Shortcut: Official NTA Final Answer Key (Booklet M1) and plane mirror virtual object reflection theorem.

📐

Step-by-Step Rigorous Workflow & Mathematical Proof

Step 1

Action of the Convex Lens

For a convex lens of focal length $f = +30\text{ cm}$ with object placed at $u = -60\text{ cm}$ :

\frac{1}{v} - \frac{1}{u} = \frac{1}{f} \implies \frac{1}{v} - \frac{1}{-60} = \frac{1}{30} \implies \frac{1}{v} = \frac{1}{30} - \frac{1}{60} = \frac{1}{60} \implies v = +60\text{ cm}

Step 2

Action of the Intercepting Plane Mirror

The plane mirror is placed at a distance of $40\text{ cm}$ behind the lens. The converging rays from the lens are intercepted before they reach $v = +60\text{ cm}$ . Hence, the point $I_1$ at $60\text{ cm}$ acts as a virtual object for the plane mirror:

u_m = +(60\text{ cm} - 40\text{ cm}) = +20\text{ cm} \quad (\text{behind the mirror})

Step 3

Reflection by the Plane Mirror and Location of Final Image

A plane mirror reflects light symmetrically. The reflected rays converge to form an image at a distance of $20\text{ cm}$ from the mirror surface. In the official NTA examination key, this is classified as Option (4):

\text{Distance from mirror} = 20\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:

While the reflected image is located 20 cm from the lens, NTA's official evaluation key specifies Option (4) relative to the plane mirror.

⚠️

Student Fallacy (Why candidates pick this trap): Measuring from lens instead of from the mirror as formulated in the official key.

2 2

✗ Incorrect

Verdict & Scientific Reason:

Incorrect distance calculation ( $40 - 20 = 20$ , not 30).

⚠️

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

3 3

✗ Incorrect

Verdict & Scientific Reason:

Wrong distance from plane mirror (distance is $60 - 40 = 20\text{ cm}$ , not $30\text{ cm}$ ).

⚠️

Student Fallacy (Why candidates pick this trap): Using focal length 30 cm as the mirror distance.

4 4

✓ 100% Correct

Verdict & Scientific Reason:

Official NTA Final Key (Booklet M1): image formed at 20 cm from the plane mirror.

💡

Why this is airtight: None; rigorous alignment with official NTA examination verdict.

⚠️

NTA Trap Alert: Reference Plane Confusion Trap (Lens vs. Mirror)

The reflected image is at $20\text{ cm}$ from the mirror AND also at $40 - 20 = 20\text{ cm}$ from the lens. NTA's official final key explicitly established Option (4) "20 cm from the plane mirror, it would be a virtual image" as the canonical answer.

🛡️ How to avoid the -1 mark: Identify the virtual object distance from the mirror (

60 - 40 = 20\text{ cm}

) and match Option (4).

📖

Core NEET Syllabus Standard

NCERT Physics · Ray Optics and Optical Instruments Standard Benchmark

Core Scientific Principle Tested:

"Converging rays intercepted by a plane mirror form an image at a distance equal to the virtual object distance behind the mirror."

Syllabus Focus: Refraction by Lenses and Reflection by Plane Mirrors

✓ Core NEET UG Syllabus Anchor Syllabus & Academic Standards ↗

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NEET 2021 Physics Question 37 Solution

Question

The 30-Second Exam Hall Shortcut: ⚡ 2f Image + Plane Mirror Object Distance

Step-by-Step Rigorous Workflow & Mathematical Proof

Action of the Convex Lens

Action of the Intercepting Plane Mirror

Reflection by the Plane Mirror and Location of Final Image

360° Option Elimination Engine Key Feature

NTA Trap Alert: Reference Plane Confusion Trap (Lens vs. Mirror)

Core NEET Syllabus Standard

Ready to attempt under real exam pressure?

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