A ray diagram finds the image by following three standard rays from the top of the object. Where the refracted rays meet, or appear to come from, the top of the image forms.
This lesson is part of SPM Physics light and optics. After drawing, you can check positions by calculation in calculating image position and magnification.
What are the three rays?
Draw the lens as a vertical line at the centre, with the principal axis horizontal and the focal points F marked on both sides at equal distances.
- Parallel ray: parallel to the axis, then through F on the far side.
- Centre ray: through the optical centre, straight on.
- Focal ray: through F on the object side, then parallel to the axis after the lens.
Bend each ray once, at the vertical line in the middle of the lens, not at the curved edge.
Worked example: object beyond 2F
An original diagram. Take a convex lens with a focal length of 10 cm and an object 3 cm tall placed 25 cm from the lens. Use a scale of 1 cm for every 5 cm.
The parallel ray and the centre ray meet on the far side between F and 2F, at about 17 cm from the lens (the formula 1/v = 1/10 − 1/25 gives 16.7 cm). The image is real, inverted, diminished and lies between F and 2F.
A screen placed at that position would show a clear small upside-down image, which is how a simple camera works.
How does the image change with the object position?
As the object moves closer to the lens, the image changes like this.
| Object position | Image |
|---|---|
| Beyond 2F | Real, inverted, diminished, between F and 2F |
| Between F and 2F | Real, inverted, magnified, beyond 2F |
| Inside F | Virtual, upright, magnified, on the same side as the object |
When the object is inside F, the refracted rays spread apart and never meet. Extend them backwards as dotted lines to find the virtual image, which is what a magnifying glass uses.
The mistake that costs marks
The common slip is to bend the rays at the curved edge of the lens, or to draw the parallel ray without passing it through the focal point. The diagram then looks plausible, but the image lands in the wrong place.
| Step | Wrong | Right |
|---|---|---|
| Where the ray bends | At the curved surface | At the vertical line through the centre |
| Parallel ray after lens | Any direction | Through the far-side F |
| Virtual image rays | Solid lines behind the lens | Dotted lines extended backwards |
A second slip is forgetting arrows on the rays. Put an arrow on each ray to show the direction of travel.
Check yourself
A convex lens has F = 8 cm. An object stands 5 cm from the lens. Describe the image and say which part of your diagram is dotted.
Answer
The object is inside F (5 cm is less than 8 cm), so the image is virtual, upright and magnified, on the same side of the lens as the object and farther from the lens than the object.
The refracted rays diverge, so the lines extended backwards to find the image are dotted. The real rays are solid.
What to study next
Put numbers to the positions with calculating image position and magnification. The lens and image-formation explorer lets you move the object and compare with your drawing.
If you want a teacher to check your diagrams as you draw them, see online one-to-one Physics tuition.