A converging lens of focal length 5cm forms a virtual image which is 20cm from the lens. How far from the lens is the object?

Analyze the question: A converging (convex) lens has a positive focal length, f = +5 cm. It forms a virtual image 20 cm from the lens. We need the object distance u.

Concept: Use the lens formula with the real-is-positive sign convention:

1/f = 1/u + 1/v

• Converging lens: f = +5 cm
• Virtual image: v is negative, so v = −20 cm

Solution:

1/u = 1/f − 1/v 1/u = 1/5 − 1/(−20) 1/u = 1/5 + 1/20 1/u = 4/20 + 1/20 = 5/20 = 1/4

u = 4 cm

Check: The object (4 cm) is inside the focal length (5 cm), which is exactly the condition for a convex lens to form a virtual, magnified, upright image. Magnification = v/u = 20/4 = 5, which makes sense for a magnifying glass.

Tip: For a convex lens, a virtual image only happens when the object is closer than f. Any option greater than 5 cm (C, D, E) can be eliminated immediately. Then just check between A and B with the formula. Also remember: virtual image means v is negative in the "real-is-positive" convention.