The distance between object and its 3 times magnified virtual image as produced by a convex lens is 20 cm . The focal length of the lens used is ______ cm .
Answer: 15
Solution
For a convex lens producing a magnified virtual image (magnification m=3, real object, virtual image on the same side): v=3u (with u negative by convention, v negative too, both on the object side). The magnitudes satisfy v−u=20 (image farther from lens than the object by 20 cm, both measured as positive distances): Taking ∣v∣=3∣u∣ and ∣v∣−∣u∣=20⇒2∣u∣=20⇒∣u∣=10 cm, ∣v∣=30 cm. Using the lens formula with signs u=−10, v=−30:
