thin lens equation

Meaning: For a lens thin enough that its thickness can be ignored, with rays near the axis, focal length f fixes where an object at distance o forms an image at distance i. Converging (convex) lenses have positive f; diverging (concave) lenses have negative f. Image distance is positive for a real image, on the side opposite the object, and negative for a virtual image, on the same side as the object.

Equation: 1/f = 1/o + 1/i, where f is focal length (m), o is object distance (m), and i is image distance (m). Magnification M = −i/o is unitless; a negative M means inverted.

On the MCAT: Setups include the eye, a magnifier or a microscope. For a converging lens and a real object, o > 2f gives a real, inverted, reduced image; f < o < 2f gives real, inverted, enlarged; o < f gives virtual, upright, enlarged. A diverging lens with a real object gives a virtual, upright, reduced image. In two-lens systems, the first image is the object for the second lens.

Common confusion: A negative i is not an error; it means a virtual image. Lenses and mirrors differ: a real image forms opposite the object for a lens but on the same side for a mirror. Also remember to invert 1/i at the end.