Parallel and focal rays in lenses

The idea

After refraction, a ray parallel to the principal axis passes through the focus of a convex lens or seems to diverge from the focus of a concave lens; a ray headed through a focus emerges parallel to the axis.

Two helpful rays

To draw the image made by a lens we use rays whose path after refraction is easy to know. One of them runs parallel to the principal axis.

A ray parallel to the principal axis passes through a convex lens. Where does it go after refraction?

• Through the principal focus on the other side
• Back the way it came
• On, parallel to the axis, unchanged

Convex and concave

Look at the red rays that come in parallel to the axis, and at the blue rays that go through (or towards) a focus. Open every tab.

Same two rules

The rules work both ways round: a parallel ray goes through the focus, and a ray through the focus comes out parallel. For the concave lens the rays only seem to pass through the focus.

After refraction, a ray parallel to the principal axis passes through the principal focus of a convex lens, or appears to diverge from the principal focus of a concave lens. A ray passing through a principal focus of a convex lens, or appearing to meet at a focus of a concave lens, emerges parallel to the principal axis.

Notes

A ray parallel to the axis goes through the focus (convex) or seems to come from it (concave). A ray through a focus (convex) or heading for it (concave) comes out parallel.

Check yourself

A ray parallel to the principal axis falls on a convex lens. After refraction it

A ray parallel to the principal axis falls on a concave lens. After refraction it

Which ray emerges parallel to the principal axis from a convex lens?

A ray appears to be heading for the principal focus of a concave lens. After refraction it

• comes out parallel to the axis again. A ray that comes out parallel is one that passed through the focus before the lens.
• passes through the principal focus on the other side — correct. Yes!
• goes through the optical centre. The ray through the optical centre is a different ray. The parallel ray goes through the principal focus.
• passes through a focus on the other side of the lens. A concave lens diverges rays. The ray only appears to come from a focus on the incoming side.
• comes out parallel to the axis. A parallel ray is bent away from the axis by a concave lens.
• appears to diverge from the principal focus on the same side as the incoming light — correct. Yes!
• A ray passing through a principal focus — correct. Yes!
• A ray parallel to the principal axis. A parallel ray is bent to pass through the focus, so it does not stay parallel.
• A ray falling on the lens very far from its centre. How far from the centre a ray falls does not decide this. A ray through a principal focus emerges parallel.
• diverges from the other focus. A ray heading for the focus comes out parallel to the axis.
• emerges parallel to the principal axis — correct. Yes!
• passes through the optical centre. Only a ray that already passes through the optical centre goes straight through it.