Illustrated Physics
physics, drawn
Concept

Magnification — where it appears

The ratio of an image's size to its object's, or of a lensed source's brightness to its unlensed brightness. The two meanings are worth keeping apart: a gravitational lens changes the second by large factors and offers no improvement at all in resolving the first.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

A converging lens making a real image. An object 2.44 focal lengths from a thin converging lens. The image sits where the construction rays cross, at 1.69 focal lengths, magnified -0.69×.

What a lens is doing, and why three rays are enough

A lens bends every ray that reaches it. The construction uses three, because three are all that can be drawn without calculation — and any three that meet prove all the rest do.

optics · Imaging A lens with no focal length. Where a ray crosses the axis, against how far off the axis it passed the deflecting body, for 1 solar mass of radius 1 solar radius. A glass lens deflects a ray by an angle proportional to its distance off axis, which is precisely the condition for every ray to arrive at one point — the flat dashed line. Gravity deflects by 4GM/c²b, which grows smaller further out, so the crossing distance goes as b² and each ray has its own focus. The grazing ray crosses at 548 astronomical units and a ray passing at 12 radii crosses at 78857; the square law is verified on the drawn curve to 1.5e-16. So there is no image plane at all, only a half-line of foci beginning at the first of those and running outward for ever. Anything placed on that line sees not an image but a ring, and moving along it does not refocus anything — it selects which rays are being seen.

The lens with no focal length

A glass lens bends a ray by an angle proportional to how far off the axis it passes, which is precisely the condition for every ray to arrive at one point. Gravity bends by an angle that falls with distance off the axis, so every ray has its own focus and there is no image plane anywhere — only a half-line of foci, beginning 548 astronomical units from the Sun and running outward for ever.

astrophysics · Light deflection Image distance against object distance. Image distance in focal lengths against object distance in focal lengths. At exactly one focal length the image runs off to infinity; inside it the image distance goes negative, which means virtual.

The focus that is a slab, not a plane

A lens images one plane and no other, which would make every photograph and every micrograph almost entirely out of focus. What rescues them is a tolerance — and there are two of them, one from rays and one from waves, which give different answers and stop being interchangeable exactly where microscopes work.

optics · Imaging

Named alongside it

The objects these essays reach for when they reach for this one.

Focal lengthImagingThe paraxial approximationReal and virtual imagesAberrationApertureCausticDiffraction limitEinstein radiusGeneral relativityGravitational lensImpact parameter

All concepts