Ray diagrams are a visual method for predicting where a lens forms an image and what that image looks like. They matter because lenses are used in eyeglasses, cameras, microscopes, telescopes, and the human eye. By drawing a few carefully chosen rays, you can determine whether an image is real or virtual, upright or inverted, and larger or smaller than the object.
This turns light behavior into a geometric problem that can be solved with a ruler and basic equations.
A converging convex lens bends parallel rays inward toward a focal point, while a diverging concave lens spreads rays outward as if they came from a focal point on the same side as the object. The three principal rays make ray diagrams reliable: one ray parallel to the axis, one through or toward the focal point, and one through the center of the lens. Where the refracted rays meet, or where their backward extensions appear to meet, marks the image location.
The lens equation and magnification equation give numerical support for the same image properties shown in the diagram.
Key Facts
- Thin lens equation: 1/f = 1/do + 1/di
- Magnification: m = hi/ho = -di/do
- For a converging lens, f is positive and parallel incoming rays pass through the far focal point.
- For a diverging lens, f is negative and parallel incoming rays spread out as if from the near focal point.
- A real image forms where refracted rays actually meet and can be projected on a screen.
- A virtual image forms where backward extensions of rays appear to meet and cannot be projected on a screen.
Vocabulary
- Converging lens
- A lens that bends parallel light rays toward the principal axis and can form real or virtual images.
- Diverging lens
- A lens that bends parallel light rays away from the principal axis and usually forms upright virtual images for real objects.
- Focal point
- The point on the principal axis where parallel rays meet or appear to originate after passing through a lens.
- Principal axis
- The straight reference line through the center of a lens and its focal points.
- Principal rays
- Special light rays used in ray diagrams because their paths through a lens are easy to predict.
Common Mistakes to Avoid
- Using the wrong focal point for the parallel ray is incorrect because a converging lens sends a parallel ray through the far focal point, while a diverging lens makes it appear to come from the near focal point.
- Drawing rays that bend at the focal point is incorrect because refraction is modeled as occurring at the lens, not at the focal point.
- Forgetting to extend diverging rays backward is incorrect because virtual images are found by tracing the refracted rays back to where they appear to meet.
- Ignoring signs in the lens equation is incorrect because positive and negative values of f and di determine whether the lens and image are converging, diverging, real, or virtual.
Practice Questions
- 1 A converging lens has focal length f = 10 cm. An object is placed 30 cm from the lens. Use 1/f = 1/do + 1/di to find the image distance and state whether the image is real or virtual.
- 2 A diverging lens has focal length f = -15 cm. An object is placed 30 cm from the lens. Find the image distance and magnification, then state whether the image is upright or inverted.
- 3 An object is placed between a converging lens and its focal point. Explain, using ray diagram reasoning, why the image is virtual, upright, and enlarged.