Mastering Lens Problems: 2025 Board Exam Solutions

Understanding Lens Problem Solutions

This analysis breaks down Question 34 from the 2025 Physics Board Exam (5 marks). After reviewing the solution video, three critical concepts emerge: lens identification, image characteristics, and lens power comparison. Students often struggle with sign conventions and practical applications, so we'll clarify these systematically.

Part 1: Concave Lens Analysis

The given lens power is -2.5D. Negative power indicates a concave lens since only diverging lenses have negative diopters. Calculate focal length using P = 1/f:

• Formula: f = 1/P = 1/-2.5 = -0.4 meters
• Convert to centimeters: -0.4 m × 100 = -40 cm

Concave lenses correct myopia (nearsightedness). The video correctly notes these lenses diverge light rays to focus images properly on the retina for myopic patients.

Part 2: Image Characteristics

With magnification (m) = -2 and object distance (u) = -20 cm (negative by sign convention):

1. Nature of Image: Negative magnification means real and inverted image. |m| = 2 indicates magnified size.
2. Height Relationship: m = hᵢ/hₒ = -2 → |hᵢ| = 2|hₒ|. Image height is double the object height.
3. Position Calculation: m = v/u → -2 = v/-20 → v = 40 cm (positive value confirms real image)
4. Height Sign: Real images are inverted, so height is negative relative to the object.

Part 3: Lens Power Comparison

For Lens A (f₁ = 10 cm) and Lens B (f₂ = 20 cm):

• Power P = 1/f (in meters)
• Convert focal lengths: f₁ = 0.1 m, f₂ = 0.2 m
• P₁ = 1/0.1 = 10D
• P₂ = 1/0.2 = 5D

Lens A has higher power (10D > 5D), meaning greater converging/diverging ability. The video emphasizes the inverse focal length-power relationship: shorter focal length = higher power.

Key Problem-Solving Framework

Step-by-Step Approach

1. Identify sign conventions: Negative power → concave lens
2. Apply formulas correctly: P = 1/f, m = v/u = hᵢ/hₒ
3. Interpret values:
   • Negative m → real/inverted image
   • |m| > 1 → magnified image
4. Compare lens power: Calculate P from f; shorter f → higher P

Common Mistakes to Avoid

• Unit errors: Focal length must be in meters for diopter calculation
• Sign confusion: Object distance (u) is always negative in lens formula
• Magnification misinterpretation: Sign indicates image orientation; magnitude indicates size ratio

Essential Concepts

• Lens Type Identification: Power sign determines converging/diverging nature
• Image Analysis: Magnification sign and value reveal image orientation and size
• Power vs. Focal Length: Inverse relationship critical for comparison questions

Action Checklist for Exam Success

1. Memorize sign conventions for lenses and mirrors separately
2. Practice unit conversions (m → cm) for focal length problems
3. Verify calculations using magnitude checks (e.g., |m| = |v|/|u|)
4. Annotate steps in solutions to demonstrate understanding
5. Review NCERT derivations for formula application contexts

Recommended Resources

• NCERT Class 12 Physics (Chapter 9): Authoritative explanations of ray optics
• Physics Wallah Optics Playlist: Practical problem-solving demonstrations
• Lens Simulation Tool (PhET Interactive): Visualize image formation scenarios

Mastering lens problems hinges on rigorous practice of sign conventions and formula applications. Which concept in this solution framework do you find most challenging to apply? Share your experience in the comments for specific troubleshooting.