Lens ray diagrams let you predict an image without algebra. By tracing a few standard rays, you can determine where the image forms and describe how it compares with the object.

What Lens Ray Diagrams Show

A lens ray diagram is a geometric sketch of how light from an object travels through a lens. The object is usually drawn as an upright arrow with its base on the principal axis, the horizontal reference line through the center of the lens. The image is found by tracing rays from the top of the object, because that top point determines the image height and orientation.

Although many rays leave the object, physicists use three principal rays because their paths are simple and predictable.

Ray-tracing comparison for a converging lens (real, inverted image formed by actual ray intersection) and a diverging lens (virtual, upright image found by backward extensions). The diagram labels the three principal rays and makes the “solid rays vs. dashed extensions” distinction visually explicit, which is the key logic your notes rely on for determining image type and orientation. Source

If the rays meet after passing through the lens, the image forms at that intersection. If the rays spread apart, you extend them backward with dashed lines to find the point where the light appears to come from.

Standard Setup for a Diagram

• Draw a straight principal axis.

• Draw the lens on the axis, centered vertically.

• Mark the focal points on both sides of the lens.

• Draw the object as an upright arrow.

• Trace at least two principal rays from the tip of the object.

• Use the third principal ray as a check.

• Draw the image from the axis to the point where the rays meet, or appear to meet.

A careful setup matters because image location, type, size, and orientation all come directly from the geometry of the sketch.

The Three Principal Rays for a Converging Lens

For a converging lens, the principal rays are drawn as follows:

• A ray parallel to the principal axis refracts through the focal point on the far side of the lens.

• A ray passing through the center of the lens continues in a straight line.

• A ray directed through the focal point on the object side emerges parallel to the principal axis after passing through the lens.

When the refracted rays actually cross on the far side of the lens, the image is real. In the diagram, the image arrow is drawn where the rays intersect. If that image arrow ends up below the principal axis while the object arrow is above it, the image is inverted.

The same diagram also shows image size. If the image arrow is taller than the object arrow, the image is enlarged. If it is shorter, the image is reduced. If the two heights match, the image is the same size as the object.

A special case occurs when the object is placed at the focal point of a converging lens. The outgoing rays are parallel, so they do not meet at a finite distance on the page. In that situation, the diagram does not show a single finite image location.

The Three Principal Rays for a Diverging Lens

For a diverging lens, the center ray is still drawn straight through the middle of the lens, but the other rays behave differently:

• A ray parallel to the principal axis refracts outward as if it came from the focal point on the same side as the object.

• A ray aimed toward the focal point on the far side of the lens emerges parallel to the axis after passing through the lens.

• A ray through the center of the lens continues essentially straight.

Because the refracted rays spread apart, they usually do not meet on the far side of the lens. To locate the image, you extend the refracted rays backward using dashed lines.

Where those dashed lines intersect is the image position. Since the light only appears to come from that point, the image is virtual rather than real.

In a diverging-lens diagram, the image is usually on the same side of the lens as the object, between the lens and the focal point. The image is also upright, because the image arrow points in the same direction as the object arrow, and it is reduced, because the image height is smaller than the object height.

Reading Image Properties from the Diagram

A correct ray diagram lets you identify each image property directly:

• Location: the position where rays intersect, or where backward extensions intersect.

• Type: real if actual rays meet; virtual if only extensions meet.

• Orientation: upright if image and object point the same way; inverted if the image is flipped relative to the object.

• Size: enlarged, reduced, or same size, based on the image height compared with the object height.

For a converging lens, the image properties change as the object position changes.

A sequence of converging-lens ray diagrams showing how the image changes as the object moves relative to $F$ and $2F$. This kind of multi-case figure is ideal for quickly reading off real vs. virtual, inverted vs. upright, and reduced vs. enlarged outcomes from geometry rather than algebra. Source

When the object is outside the focal point, the diagram shows a real, inverted image. Depending on the exact object position, that image can be reduced, enlarged, or the same size. When the object is inside the focal point, the rays do not cross after the lens, but their backward extensions do. The diagram then shows a virtual, upright, enlarged image.

For a diverging lens, the ray pattern is more consistent. The backward extensions always meet on the object side, so the image remains virtual and upright, and the geometry of the diagram shows it as reduced.

Common Mistakes in Lens Ray Diagrams

Several errors can lead to the wrong image properties:

• Starting rays from the middle of the object instead of the tip.

• Forgetting to mark the focal points before drawing rays.

• Sending a converging-lens parallel ray through the wrong focal point.

• Forgetting that dashed lines are only backward extensions, not actual traveling light.

• Drawing the center ray with a bend at the middle of a thin lens.

• Judging size by guesswork instead of comparing image and object heights on the sketch.

Another common mistake is assuming that every image on the far side of a lens must be real or that every upright image must be virtual. The diagram itself must decide the answer. Actual ray intersections produce real images, while intersections of dashed extensions produce virtual images. Good ray diagrams are logical tools for determining image location, type, size, and orientation from the three principal rays.