Draw a simple lens image

To draw the image formed by a converging lens, draw two rays from the tip of the object. Draw one parallel to the axis that bends through the principal focus, and one through the optical centre that goes straight on. Where the rays meet is the image of that point.

This skill uses the bending of light from refraction, drawn in a simple way with one sharp bend at the centre line of the lens. It is part of light and imaging.

What do the lens terms mean?

A converging lens (thicker in the middle) brings parallel rays to a point. The principal axis is the line through the centre of the lens, at 90° to it. The optical centre is where the axis crosses the lens.

The principal focus, F, is the point where rays parallel to the axis meet after the lens. The focal length, f, is the distance from the centre of the lens to F.

There is a principal focus on each side of a thin lens, both at distance f. Draw the lens as a vertical line with small arrowheads, mark F on each side, and use the same scale along and across the axis.

How do I construct the image, step by step?

1. Draw the axis and lens, then mark F on both sides at the focal length.
2. Draw the object as an upright arrow standing on the axis, at its distance from the lens.
3. Ray 1: from the tip of the object, draw a ray parallel to the axis to the lens line, then bend it to pass through F on the far side.
4. Ray 2: from the tip of the object, draw a ray through the optical centre. It goes straight on without bending.
5. Mark the image point where the two rays meet, and draw the image arrow down to the axis.
6. Add arrows on the rays. Then measure the image distance from the lens and the image height.

A third standard ray goes from the tip of the object through the near F, hits the lens, and emerges parallel to the axis. It is a useful check but not needed if two rays already meet.

Worked example

An object 3.0 cm tall stands 12.0 cm from a converging lens of focal length 4.0 cm. (Invented example data.) Construct the image and describe it.

Step 1, set up: axis horizontal, lens as a vertical line, F marked 4.0 cm either side, object 12.0 cm to the left.

Step 2, ray 1: from the tip of the object, a ray parallel to the axis meets the lens 3.0 cm above the axis. It then bends down through F on the right, 4.0 cm beyond the lens.

Step 3, ray 2: from the tip of the object, a ray through the optical centre goes straight on, sloping down.

Step 4, find the meeting point: a careful scale drawing shows the rays meeting about 6.0 cm beyond the lens, 1.5 cm below the axis.

Step 5, describe: the image is 6.0 cm from the lens on the opposite side, 1.5 cm tall, upside down and smaller than the object. The magnification is 1.5 ÷ 3.0 = 0.5.

Step 6, check: the rays really meet, so the image is real and can be shown on a screen. An object beyond 2f (here 2f = 8 cm) should give a smaller, inverted, real image between f and 2f, and 6.0 cm lies between 4 cm and 8 cm. The description is consistent.

The mistake to watch for

A frequent drawing error is to bend the parallel ray through the focus on the wrong side, or to let the ray through the centre bend.

Mistaken diagram: the parallel ray bends to pass through the focus on the same side as the object.

A converging lens bends rays toward the axis on the far side, so the ray must pass through F after the lens.

The correction is a simple rule: the ray that arrives parallel goes through the far-side focus, and the ray through the centre does not bend. If your two rays do not meet, recheck that both bend or pass through the correct point. Also make sure both rays start at the tip of the object, not the base.

Check yourself

Try these on graph paper, then open each answer.

1. An object is placed at 2f from a converging lens of focal length 5.0 cm. Where is the image and how big is it?

2. Which standard ray goes through a lens without bending?

3. An object 2.0 cm tall is 8.0 cm from a converging lens of focal length 5.0 cm. Draw two rays. Is the image larger or smaller than the object, and is it inverted?

Where this leads next

The next lesson decides when an image is real and when it is virtual, and how the dashed lines change: real and virtual image construction. Then use the light and imaging practice set to mix the skills.

Some students follow every step in class but freeze when a blank page has to be turned into a neat ray diagram. Our teachers use live drawing in online one-to-one Physics tuition to build exactly that confidence.