thin lenses
Summary
A thin lens is an idealized lens whose thickness is negligible, so light bends at a single plane. Image position follows 1/f = 1/o + 1/i, with f positive for converging and negative for diverging lenses. A converging lens gives a real or a virtual image depending on whether the object is beyond or inside f.
Detail
Meaning: A thin lens is an idealization: its thickness is negligible next to its focal length and the object and image distances, so the bending of light is treated as occurring at a single plane. A converging (convex) lens brings parallel rays to a real focus; a diverging (concave) lens spreads them as if they came from a virtual focus.
Equation: 1/f = 1/o + 1/i, with m = −i/o. Here f is focal length (m), o is object distance (m), i is image distance (m), and m is magnification (unitless). Power is P = 1/f in diopters (m⁻¹), and powers of thin lenses in contact add.
On the MCAT: Sign conventions drive the questions. f is positive for converging and negative for diverging lenses. i is positive for a real image (opposite side of the lens from the object) and negative for a virtual one. A negative m means inverted. A converging lens with o < f gives a virtual, upright, enlarged image (a magnifying glass); with o > 2f it gives a real, inverted, reduced image.
Common confusion: Mirror rules do not transfer. A real image forms on the opposite side of a lens from the object, but on the same side as the object for a mirror. A converging lens also does not always make a real image; it depends on whether o exceeds f.
Sources
- Physics (Giancoli)
- Fundamentals of Physics (Halliday, Resnick, Walker)
- Physics (Cutnell and Johnson)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.