Lenses and their images

A lens is a piece of transparent material (usually glass) with at least one curved surface.

• A convex lens is thicker in the middle. It converges light: brings parallel rays together.
• A concave lens is thicker at the edges. It diverges light: spreads parallel rays apart.

Its two surfaces are parts of two spheres, so a lens has two centres of curvature (C₁ and C₂), a principal axis through them, an optical centre O in the middle, and two principal foci, F₁ and F₂, one on each side.

Hold a convex lens up to the Sun and focus the bright spot on a sheet of paper: the paper can start to burn. The spot is an image of the Sun, and its distance from the lens is about the focal length.

Drawing rays through a lens (take the ray to the middle of the lens before bending it):

• parallel to the axis → passes through F₂ (or seems to come from F₁ for a concave lens);
• through F₁ → comes out parallel to the axis;
• through O → goes straight on, undeviated.

Convex lens: move the object closer step by step (Table 9.4):

As the object comes closer, the image moves further away and grows. Once the object is inside F₁, the image suddenly appears on the same side, upright and big: that is how a magnifying glass works.

A concave lens always gives a virtual, erect, smaller image, on the same side as the object (Table 9.5).

A handy link: a convex lens behaves like a concave mirror, and a concave lens like a convex mirror.