Converging Lenses and Ray Diagrams

A converging (convex) lens is thicker in the middle than at the edges. Parallel rays passing through converge to a single point called the principal focus (focal point).

Key terms

Term	Definition
Principal focus ($F$)	The point where rays parallel to the principal axis converge after passing through the lens
Focal length ($f$)	The distance from the centre of the lens to the principal focus
Principal axis	The straight line through the centre of the lens, perpendicular to the lens

Drawing ray diagrams

To locate an image, draw at least two of these three standard rays from the top of the object:

1. Parallel ray: travels parallel to the principal axis, then refracts through $F$ on the other side.
2. Central ray: passes straight through the centre of the lens without bending.
3. Focal ray: passes through $F$ on the object side, then refracts parallel to the principal axis.

The image forms where the rays (or their extensions) intersect.

Image properties at different object positions

Object position	Image	Properties
Beyond $2F$	Between $F$ and $2F$	Real, inverted, diminished
At $2F$	At $2F$	Real, inverted, same size
Between $F$ and $2F$	Beyond $2F$	Real, inverted, magnified
At $F$	At infinity	No image (rays emerge parallel)
Between $F$ and lens	Same side as object	Virtual, upright, magnified (magnifying glass)

Worked example

An object is placed between $F$ and $2F$ of a converging lens. Describe the image.

The image is real (rays actually converge), inverted (upside down), magnified (larger than the object), and formed beyond $2F$ on the other side of the lens.

Common errors and how to correct them

Drawing the refraction at both surfaces of the lens. In ray diagrams, draw the refraction occurring at the centre line of the lens (one bend), not at each surface.

Confusing real and virtual images. A real image is formed where rays actually meet; it can be projected on a screen. A virtual image is formed where rays appear to diverge from; it cannot be projected.

How to apply this in an exam

Use a ruler for ray diagrams. Draw at least two rays. Clearly mark $F$ and $2F$ on both sides of the lens. Describe the image using all four properties: real/virtual, upright/inverted, magnified/diminished/same size, and its position.