Intermediate · 13 min
Images formed by converging lenses
Find real image positions and magnification using a thin-lens model.
Focus parallel rays
A converging lens brings rays parallel to its principal axis towards a focal point. The distance from a thin lens to that point is the focal length f. With a real object farther away than f, the lens can form a real image on the opposite side. A ray parallel to the axis passes through the far focal point after refraction; a ray through the thin lens's centre is approximately undeviated.
Worked example
An object placed at twice the focal length produces a real, inverted image at twice the focal length on the other side of an ideal thin converging lens.
Position and size
For the real-object, real-image cases here, use positive distances and 1/f = 1/u + 1/v. Here u is object distance and v is image distance, both measured from the lens. Magnification magnitude is |M| = v/u = image height/object height. These real images are inverted; the positive magnitude describes size only. Keep all distances in the same unit and stay within the thin-lens approximation.
Worked example
For f = 8 cm and u = 24 cm: 1/v = 1/8 − 1/24 = 1/12, so v = 12 cm Magnification magnitude = 12 ÷ 24 = 0.5
Check a lens diagram
- For a thin converging lens with f = 5 cm and an object at u = 10 cm, calculate the image distance and magnification magnitude.
- Draw two principal rays and check that they meet at your calculated image position.