Convex Lens Ray Diagram: How to Draw All 6 Object Positions

A convex lens ray diagram is the quickest way to find where an image forms and what it looks like. You draw three principal rays from the top of the object: the parallel ray bends through the focal point F, the focal ray comes out parallel, and the centre ray goes straight. Where the refracted rays meet — or appear to meet — is the image. The diagrams for all six object positions use the same three rays; only the object's location changes. This guide walks through every case step by step.

Imagine a crowd of people walking side by side. When they hit a patch of sand at an angle, the ones who reach the sand first slow down first, and the whole line pivots. That is exactly how a convex lens bends light — slower in the glass, faster in air — and where the rays end up tells you everything about the image. Our full convex lens guide covers the basics of how the lens works; this guide focuses purely on the diagrams.

The three principal rays for any convex lens ray diagram

Every convex lens ray diagram uses the same three rays. Memorise them and you can draw any case:

Ray 1 — parallel ray. From the top of the object, draw a ray parallel to the principal axis. When it hits the lens, refract it so it passes through the focal point F on the far side. This is a converging lens — parallel in, through focus out.

Ray 2 — focal ray. From the top of the object, draw a ray that passes through the focal point F on the near side (the object's side) on its way to the lens. When it hits the lens, refract it so it travels parallel to the principal axis. Think of it as the reverse of Ray 1.

Ray 3 — centre ray. From the top of the object, draw a ray straight through the optical centre of the lens. It does not bend. For a thin lens, this ray continues in a straight line because the two curved surfaces cancel each other's refraction at the centre.

The image of the object top is where the three refracted rays intersect. If they diverge after the lens, trace them backwards — the virtual intersection point is still the image. Our concave vs convex lens comparison explains why convex lenses produce converging rays while concave lenses produce diverging ones.

Step-by-step method to draw any convex lens ray diagram

Here is the general method. It works for every object position.

1. Draw the lens and axis. Sketch a vertical line for the lens. Draw a horizontal principal axis through its centre. Mark the optical centre O where they cross.
2. Mark the focal points. Mark F at the focal length distance on both sides. Mark 2F at twice that distance on both sides.
3. Draw the object. Draw an upright arrow at the correct object distance. The arrow's base sits on the principal axis.
4. Draw Ray 1 (parallel). From the arrow tip, a ray parallel to the axis. At the lens, bend it through F (far side).
5. Draw Ray 2 (focal). From the arrow tip, a ray through F (near side). At the lens, bend it parallel to the axis.
6. Draw Ray 3 (centre). From the arrow tip, a ray through O — it goes straight.
7. Find the image. Where the refracted rays converge (real image) or appear to diverge from (virtual image), draw the image arrow.

A real image sits on the opposite side of the lens and is inverted. A virtual image sits on the same side as the object and is upright.

All 6 object positions in a convex lens ray diagram

1. Object at infinity

The object is so far away that incoming rays are effectively parallel. This is the simplest case.

• Ray 1 (parallel) goes straight to the lens and refracts through F.
• Ray 2 and 3 are not drawn separately — at infinity, all rays are effectively parallel to the axis.
• The refracted rays converge at F. The image is a point-sized dot at F.

Image: real, inverted, highly diminished, at F. This is how a telescope objective lens collects starlight.

2. Object beyond 2F (between infinity and 2F)

This is the most common case in cameras and the human eye when looking at distant objects.

• Ray 1: parallel in, through F (far side).
• Ray 2: through F (near side), parallel out.
• Ray 3: straight through O.
• The three refracted rays meet between F and 2F on the far side.

Image: real, inverted, diminished (smaller than the object), located between F and 2F on the far side.

3. Object at 2F

Here the object distance is exactly twice the focal length.

• All three rays follow the same logic.
• The refracted rays meet at 2F on the far side.
• The image is exactly the same size as the object.

Image: real, inverted, same size, at 2F on the far side. Useful for 1:1 imaging systems.

4. Object between 2F and F

The object sits between twice the focal length and the focal point itself.

• Same three rays. The refracted rays now converge beyond 2F on the far side.
• The image is larger than the object.

Image: real, inverted, magnified, beyond 2F on the far side. This is how a projector works — the slide sits between F and 2F, and the enlarged image appears on the screen.

5. Object at F

This case is a trick. When the object sits exactly at the focal point:

• Ray 1: parallel in, through F on the far side.
• Ray 2: goes through F on the near side — but the object is already at F, so this ray is parallel to the axis before it enters the lens. After the lens, it refracts parallel.
• Ray 3: straight through O.
• The refracted rays emerge parallel to each other. They never converge, and they never appear to diverge from a point.

Image: no image formed (image at infinity). In practice, you get a highly blurred, over-magnified mess.

6. Object between F and O (inside F)

This is the magnifying glass case. The object is closer to the lens than the focal point.

• Ray 1: parallel in, through F (far side).
• Ray 2: from the object tip, a ray heading toward F (near side) — but since the object is inside F, this ray would need to go backwards to reach F. Instead, draw a ray that appears to come from F on the near side: it enters the lens and emerges parallel.
• Ray 3: straight through O.
• After the lens, all three refracted rays diverge. Trace them backwards — they meet on the object's side.

Image: virtual, upright, magnified, on the same side as the object. This is exactly what a magnifying glass does.

The HyperPhysics ray diagram guide provides interactive examples of all these cases with adjustable object positions.

Quick reference table

Common mistakes in convex lens ray diagrams

Drawing the focal ray backwards. The focal ray must go through the focal point on the object's side on its way to the lens. Many students draw a ray that starts at the focal point — that is not right. The ray only needs to pass through F, not originate there.

Forgetting arrowheads. Light travels from object to lens to image. Every ray segment needs an arrowhead showing direction.

Curved rays after the lens. Refracted rays are straight lines. They change direction at the lens surface but are straight on each side. Do not curve them.

Assuming the lens is infinitely thin. The thin-lens approximation works fine for most school problems. It assumes the lens has negligible thickness so that ray bending happens at a single plane.

Worked example: object at 2F

Draw a convex lens ray diagram for an object placed at 2F, where the focal length is 10 cm.

Place the lens at the centre. Mark O at the lens centre. Mark F at 10 cm on both sides and 2F at 20 cm on both sides. Draw the object as an arrow, 2 cm tall, at 20 cm on the left.

• Ray 1: from the arrow tip, parallel to the axis. At the lens, refract it through F (right side at 10 cm).
• Ray 2: from the arrow tip, through F (left side at 10 cm). At the lens, refract it parallel to the axis.
• Ray 3: from the arrow tip, straight through O.

The three refracted rays meet at 20 cm on the right side — exactly at 2F. The image arrow is 2 cm tall and inverted.

Magnification = image height / object height = 2/2 = 1. The image is same size.

The OpenStax college physics section on image formation provides a deeper look at the mathematics behind these ray diagrams, including the thin-lens equation.

Summary

A convex lens ray diagram uses three principal rays — parallel, focal, and centre — to determine image position, size, orientation, and type. The six object positions produce four types of real images (at infinity, beyond 2F, at 2F, between 2F and F), one no-image case (at F), and one virtual image (inside F). The method is always the same: draw the three rays, find where they meet, and read off the characteristics. For a detailed explanation of how the lens itself bends light, see our convex lens guide. To understand how diverging lenses differ, see the concave lens guide.