Physics Problem 9.23: Optimal Magnification Distance
Find the optimal distance to hold a magnifying glass (f = 9cm) from a card sheet to achieve maximum magnifying power with distinct vision.
Object Distance
9.0 cm
Image Distance
-∞ cm
Magnification
2.78×
Status
Adjusting
Given Values
- Focal length (f): 9 cm
- Near point (D): 25 cm
- Square size: 1 mm²
Key Formulas
Lens Formula: 1/f = 1/v - 1/u
Angular Magnification: M = 1 + D/f
Optimal Distance: u = f×D/(f+D)
Solution
For maximum magnifying power, the virtual image should be formed at the near point (25 cm). The optimal object distance is 6.43 cm, giving a maximum magnification of 3.78×.
