6.10 Thin Lenses

The Thin Lens Equation

For thin lenses, 1/f = 1/d_o + 1/d_i, where f is focal length, d_o is object distance, and d_i is image distance. Converging (convex) lenses have positive f; diverging (concave) lenses have negative f. Solve for d_i to locate the image, then use magnification m = -d_i/d_o = h_i/h_o to find image height and orientation.

Real vs. Virtual Images

A positive d_i means a real image forms on the opposite side of the lens from the object (light actually converges there) — it can be projected on a screen. A negative d_i means a virtual image forms on the same side as the object, appearing upright and cannot be projected. Sign of m tells orientation: negative m = inverted, positive m = upright.

Ray Diagrams & Lens Behavior

Ray diagrams use two principal rays: one parallel to the axis bending through the focal point, and one through the lens center undeviated. Converging lenses form real, inverted images when d_o > f, and magnified virtual upright images when d_o < f. Diverging lenses always form virtual, upright, reduced images regardless of object distance.

Key terms

Thin lens equation

1/f = 1/d_o + 1/d_i, relating focal length, object distance, and image distance.

Magnification formula

m = -d_i/d_o = h_i/h_o; negative m means inverted image, positive m means upright.

Real image

Forms where light rays actually converge; positive d_i; can be projected on a screen; typically inverted.

Virtual image

Forms where light rays appear to diverge from; negative d_i; cannot be projected; typically upright.

Diverging lens image properties

Always produces virtual, upright, and reduced images regardless of object distance.

Try an AP-style question

A diverging lens has f = −20 cm, and an object is 20 cm away. Where is the image?

1. 20 cm on the other side (real)
2. 40 cm on the object's side
3. No image forms
4. 10 cm on the object's side (virtual)