5.3 Images from Lenses

The thin lens equation

For a thin lens, 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. This equation predicts where an image forms and whether it's real or virtual.

Magnification and image properties

Magnification m = -d_i/d_o = h_i/h_o. If |m| > 1, the image is enlarged; if |m| < 1, it's reduced. A negative m means the image is inverted; positive means upright. Positive d_i indicates a real image (opposite side, light converges); negative d_i indicates a virtual image (same side as object, light appears to diverge from it).

Ray diagrams for lenses

Use principal rays to locate images: a ray parallel to the axis refracts through the far focal point (converging lens); a ray through the near focal point emerges parallel; a ray through the center passes straight through. Converging lenses can form real inverted images (object beyond f) or virtual upright magnified images (object inside f). Diverging lenses always form virtual, upright, reduced images.

Key terms

Thin lens equation

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

Magnification (lens)

m = -d_i/d_o = h_i/h_o; negative m = inverted image, |m|>1 = enlarged.

Real image (lens)

Forms when light rays actually converge; positive d_i; located on the opposite side of the lens from the object.

Virtual image (lens)

Forms when refracted rays appear to diverge from a point; negative d_i; located on the same side as the object.

Diverging lens images

Always virtual, upright, and reduced in size, regardless of object position.

Try an AP-style question

An object is 30 cm from a converging lens with f = 10 cm. Where is the image?

1. 7.5 cm on the other side
2. 30 cm on the other side
3. 15 cm on the other side
4. 20 cm on the same side