An object placed 15cm from a converging lens forms a real image whose magnification is 2.0. What is the focal length of the lens?

Analyze the question: A converging lens forms a real image of an object 15 cm away. Magnification is 2.0. We need the focal length.

Concept:

• Magnification: m = v/u (magnitude), so for a real image, v = m × u
• Lens formula (real-is-positive): 1/f = 1/u + 1/v

Solution:

1. Find the image distance: v = m × u = 2.0 × 15 = 30 cm

2. Apply the lens formula: 1/f = 1/15 + 1/30 1/f = 2/30 + 1/30 = 3/30 = 1/10

3. So f = 10 cm

Check: Using f = uv/(u + v) = (15 × 30)/(15 + 30) = 450/45 = 10 cm ✓

Note that a real image from a converging lens is inverted and on the opposite side of the lens, and the object must be between f and 2f. Here f = 10 cm and u = 15 cm, which is between 10 and 20 cm, so the result is consistent.

Answer: B (10.00 cm)

Exam tip: For real images, use the quick formula f = m·u/(m + 1). Here f = (2 × 15)/3 = 10 cm. This saves time in the exam.