Thin Lens & Mirror
Image position and magnification for lenses and curved mirrors, with a principal-ray diagram. One sign convention throughout, stated below and used by every number on the page.
Element
Distances and heights share it, so magnification never depends on which you pick.
Always a magnitude. The element type gives it its sign.
Object
Sign convention
real is positive
One equation covers all four elements: 1/u + 1/v = 1/f, with m = −v/u.
- u
- Always positive: the object stands in front of the element.
- f
- Positive for a converging lens or a concave mirror, negative for a diverging lens or a convex mirror.
- v
- Positive means a real image — behind a lens, in front of a mirror. Negative means a virtual one, on the other side.
- m
- Positive is upright, negative inverted, |m| > 1 enlarged.
The Cartesian convention writes the same physics with a negative object distance and a different equation for mirrors. Mixing the two is where the signs go wrong, so this page uses only the one above.
Image distance
— cm
The three principal rays
- Parallel to the axis in, through the focal point out.
- Straight through the centre, undeviated.
- Through the focal point in, parallel to the axis out.
Dashed lines are construction, not light: where the image is virtual the rays never meet, and it is their backward extensions that cross. The image arrow is dashed and hollow when it is virtual.
- Magnification
- —
- Image height
- —
- Nature
- —
- Orientation
- —
- Size
- —
- Optical power
- — D
Negative is inverted
Magnification against object distance
m vs u
Where the curve breaks, the object is at the focal point and the magnification is unbounded. It changes sign across that break: an object further out than f gives an inverted image, one inside it an upright one.