Principal foci and focal length

The idea

Rays parallel to the principal axis converge to (convex lens) or appear to diverge from (concave lens) a point, the principal focus; a lens has two, F1 and F2, and focal length f is their distance from O.

Sunlight and a lens

Parallel rays of light from a far away object fall on a convex lens. They come together in a small bright spot behind the lens.

If the rays came from the other side of the lens instead, where would they meet?

• At another focus, on the opposite side
• At the same spot as before
• They would not meet anywhere

Parallel rays

Try the convex lens with light from the left and from the right. Then try the concave lens. Change f too.

Two foci

The convex lens brought the rays together at a point. The concave lens made them seem to come from a point. Light from the other side gave the second focus. In every case the focus was f away from O.

Rays parallel to the principal axis converge to a point on the axis (convex lens) or appear to diverge from a point on the axis (concave lens). This point is the principal focus. A lens has two, F₁ and F₂. The focal length f is the distance of a principal focus from the optical centre O.

Notes

Parallel rays converge to (convex) or seem to diverge from (concave) the principal focus. A lens has two, F₁ and F₂, and the focal length f is the distance of a focus from O.

Check yourself

Rays parallel to the principal axis pass through a convex lens. After refraction they

Parallel rays pass through a concave lens. After refraction they

How many principal foci does a lens have?

The focal length of a lens is the distance between

• converge to a point on the principal axis — correct. Yes!
• diverge, seeming to come from a point on the axis. That is what a concave lens does to parallel rays.
• stay parallel to each other. A convex lens converges the parallel rays to the principal focus.
• meet at a point on the other side of the lens. A concave lens does not bring rays together. They spread out as if from a point on the axis.
• appear to diverge from a point on the principal axis — correct. Yes!
• pass on without any change of direction. A concave lens diverges parallel rays; only a ray through the optical centre goes straight on.
• One. Rays coming from the other side of the lens give a second principal focus, so a lens has two.
• Four. A lens has two principal foci, F₁ and F₂.
• Two, F₁ and F₂, one on each side of the lens — correct. Yes!
• a principal focus and the optical centre — correct. Yes!
• the two principal foci. That is twice the focal length. Focal length is measured from the optical centre to a focus.
• the object and the lens. That is the object distance, not the focal length.