Magnification: \$m = \frac{h'}{h} = -\frac{v}{u}\$ where \$h'\$ is image height and \$h\$ is object height.
Sign convention (Cartesian):
Object distance \$u\$ is negative (object is on the incoming‑light side).
Image distance \$v\$ is positive for real images (formed on the opposite side) and negative for virtual images.
Focal length \$f\$ is positive for converging lenses.
Image Characteristics for Different Object Positions
Object Position
Relation to Focal Length
Image Position (\$v\$)
Image Size
Orientation
Nature
Beyond \$2f\$ (farther than twice the focal length)
\$u > 2f\$
Between \$f\$ and \$2f\$ (real, on opposite side)
Reduced (\$|m| < 1\$)
Inverted
Real
At \$2f\$ (centre of curvature)
\$u = 2f\$
At \$2f\$ (real)
Same size (\$|m| = 1\$)
Inverted
Real
Between \$f\$ and \$2f\$
\$f < u < 2f\$
Beyond \$2f\$ (real)
Magnified (\$|m| > 1\$)
Inverted
Real
At \$f\$ (object at focal point)
\$u = f\$
Image at infinity (parallel rays)
Highly magnified (theoretically infinite)
Inverted
Real (practically not formed)
Inside \$f\$ (closer than focal length)
\$0 < u < f\$
Virtual, on same side as object
Magnified (\$|m| > 1\$)
Upright
Virtual
Ray Diagram Description
To construct a ray diagram for a converging lens, use three principal rays:
Parallel Ray: A ray parallel to the principal axis emerges from the lens passing through the focal point on the opposite side.
Focal Ray: A ray directed towards the focal point on the object side emerges from the lens parallel to the principal axis.
Centre Ray: A ray passing through the optical centre of the lens continues in a straight line without deviation.
The point where the refracted rays intersect (or appear to intersect) determines the image position, size, and nature.
Suggested diagram: Ray diagram for a converging lens showing the three principal rays for an object placed between \$f\$ and \$2f\$, producing a real, inverted, magnified image beyond \$2f\$.
Practical Applications
Camera lenses (real, inverted images recorded on film or sensor).
Magnifying glasses (object placed within \$f\$, producing a virtual, upright, magnified image).
Projectors (object placed beyond \$f\$, projecting a real, inverted image onto a screen).
Common Misconceptions
“All images formed by converging lenses are inverted.” – Not true for objects placed within the focal length; those produce upright virtual images.
“A larger object always gives a larger image.” – Image size also depends on object distance; a small object far from the lens can produce a larger image than a larger object placed near the focal point.
“The focal length changes with object distance.” – The focal length is a property of the lens and remains constant for a given medium.
Summary Checklist
Identify the object distance relative to \$f\$ and \$2f\$.
Use the lens formula to calculate image distance \$v\$.
Calculate magnification \$m = -v/u\$ to determine size and orientation.
Classify the image as real or virtual, upright or inverted, magnified or reduced.