Convex lens ray diagram: how to draw it
The short answer. A convex lens ray diagram comes down to three rules. ① A ray parallel to the optical axis refracts through the focal point on the far side. ② A ray through the centre of the lens goes straight through. ③ A ray through the near focal point emerges parallel to the optical axis. Draw any two of them and find where they cross — that gives you the position and size of the image. And the rule that decides everything: if the object is outside the focal point the image is real (inverted); if it is between the focal point and the lens the image is virtual (upright and magnified).
1. Before you draw: mark the optical axis, both focal points and 2F
Most mistakes happen before the first ray is drawn. Always add these three things to the diagram yourself:
- The optical axis — the horizontal line through the centre of the lens. Everything else is measured against it.
- The focal point F — it exists on both sides of the lens, at equal distance from the centre. Drawing only one is what makes students send the refracted ray the wrong way.
- The point 2F (twice the focal length) — the boundary between an image smaller than the object and one larger than it. Mark it even when the question does not mention it.
2. The three ray-tracing rules
① Ray parallel to the optical axis → refracts through the far focal point
From the tip of the object, draw a line parallel to the optical axis up to the lens. There it bends and must pass through the focal point F on the other side. "Light that arrives parallel is collected at the focus" is, in essence, what a converging lens is.
② Ray through the centre of the lens → goes straight through
The ray from the tip of the object to the centre of the lens is not deviated. It takes one straight edge to draw, so always use it. It also doubles as a check on whether your first ray was drawn correctly.
③ Ray through the near focal point → emerges parallel to the axis
This is the reverse of ①. A ray that enters via the near focal point F leaves the lens parallel to the optical axis. Keep it as a spare ray for when the intersection of ① and ② falls off the edge of the page.
Two rays are enough. You do not need all three. ① and ② are the fastest and the most reliable. If you do draw all three and they fail to meet at a single point, one of them is wrong — which makes the third ray a useful check.
3. Object position and image type (summary table)
Almost every exam question is really asking which row of this table you are in. Build the diagram first, then confirm it against the table.
| Object position | Image type | Orientation | Size | Where it forms |
|---|---|---|---|---|
| Beyond 2F | Real | Inverted | Smaller than the object | Between F and 2F on the far side |
| Exactly at 2F | Real | Inverted | Same as the object | At 2F on the far side |
| Between 2F and F | Real | Inverted | Larger than the object | Beyond 2F on the far side |
| Exactly at F | No image forms (the refracted rays leave parallel and never intersect) | |||
| Between F and the lens | Virtual | Upright | Larger than the object | On the same side as the object (seen through the lens) |
4. Real image vs virtual image
A real image forms where light genuinely converges. That is why it can be caught on a screen, and why it appears inverted.
With a virtual image the light never converges: what intersect are the backward extensions of the refracted rays. It can only be looked at, never projected. That is exactly what happens when you read small print through a magnifying glass — the image is upright and magnified.
In one sentence: object outside the focal point → real, inverted image; object inside the focal point → virtual, upright, magnified image. Checking that position before you draw removes half of all mistakes.
5. Four very common mistakes
- Drawing the focal point on one side only. A convex lens has a focal point on the left and on the right. Ray ① heads for the focal point on the far side.
- Starting the rays from the base of the object. They start from the tip. The base sits on the optical axis, so the base of the image lands on it too.
- Bending the ray twice, once at each lens surface. At this level you draw a single deviation, at the centre line of the lens.
- Believing that covering half the lens cuts the image in half. It does not — the image only gets dimmer. Countless rays reach each point of the image; drawing just two rays is what creates this misconception.
6. Frequently asked questions
How many rays do I need to memorise?
Three: the ray parallel to the axis refracts through the far focal point, the ray through the centre goes straight, and the ray through the near focal point emerges parallel to the axis. Any two are enough to construct the image.
How do I tell a real image from a virtual image?
Object farther than the focal point → real, inverted image that can be projected onto a screen. Object between the focal point and the lens → virtual, upright, magnified image that cannot be projected. That is the magnifying-glass case.
What happens if the object is exactly at 2F?
A real, inverted image of the same size forms at 2F on the far side. The point 2F is the boundary between an image smaller and an image larger than the object.
Is an image formed if the object sits exactly at the focal point?
No. All refracted rays leave parallel to the optical axis and never cross. This case comes up often in exams.
What if I cover the lower half of the lens?
The image keeps its shape and simply becomes dimmer. Many rays reach every point of the image, so blocking part of the lens only reduces the amount of light collected.
Is there a free simulator I can practise with?
Optics Craft is a browser-based optics simulator: drag the object, the lens or the focal points and the rays and image are recalculated in real time. Nothing to install, and the demo on the landing page is free.
Check the rules by moving things yourself
In Optics Craft you drag the object, the lens or the focal points and watch the rays and the image follow. "The instant the object crosses inside the focal point, the image turns virtual" — instead of memorising the table, you see it happen.
🔬 Try the free demoFull access for ¥980 per year (about US$7) ／ Nothing to install — runs in your browser