Locating an image using light rays is fundamentally about tracing the path of light from an object through an optical system (like a mirror or lens) to determine where those rays converge or appear to originate. The image is precisely where these rays either physically intersect or where they seem to intersect if extended backward.
The Core Principle of Image Formation
Images are always located by extending diverging rays back to a point at which they intersect. This point signifies the image's position. Essentially, images are located either at a point from which the rays of light actually diverge (forming a real image) or at a point from which they appear to diverge (forming a virtual image).
Ray Tracing: A Step-by-Step Guide
Ray tracing is a graphical method used to determine the characteristics (location, size, orientation, type) of an image formed by mirrors or lenses. It involves drawing specific "principal rays" whose paths are known and predictable.
Here's how to apply ray tracing:
- Select Principal Rays: For any point on an object (typically the top), draw at least two, but preferably three, principal rays. These rays have predictable behaviors when they interact with the optical element.
- Ray 1 (Parallel Ray): A ray traveling parallel to the principal axis of the mirror or lens.
- For a converging lens/concave mirror: After refraction/reflection, it passes through the focal point (F).
- For a diverging lens/convex mirror: After refraction/reflection, it appears to come from the focal point (F) on the same side.
- Ray 2 (Focal Ray): A ray passing through (or directed towards) the focal point (F) of the optical element.
- For a converging lens/concave mirror: After refraction/reflection, it travels parallel to the principal axis.
- For a diverging lens/convex mirror: A ray that is directed toward the focal point on the opposite side of the lens will emerge parallel to the principal axis. For a convex mirror, a ray directed towards the focal point behind the mirror will reflect parallel to the principal axis.
- Ray 3 (Center Ray): A ray passing through the optical center of a lens or the center of curvature (C) of a mirror.
- For a lens: A ray passing through the optical center continues undeviated.
- For a mirror: A ray passing through the center of curvature reflects back along its original path.
- Ray 1 (Parallel Ray): A ray traveling parallel to the principal axis of the mirror or lens.
- Draw Refracted/Reflected Rays: Based on the type of mirror or lens, draw the path of each principal ray after it interacts with the optical element.
- Locate the Intersection:
- If the actual refracted or reflected rays intersect at a point, that point is the location of a real image.
- If the refracted or reflected rays diverge, extend them backward (as dashed lines) until they intersect. The point where these backward extensions meet is the location of a virtual image.
Understanding Real vs. Virtual Images
The nature of the image—whether it's real or virtual—is determined by how the light rays interact at the image point.
| Feature | Real Image | Virtual Image |
|---|---|---|
| Ray Intersection | Formed where actual light rays converge and pass through the image point. | Formed where light rays appear to diverge from the image point (when extended backward). |
| Projection | Can be projected onto a screen. | Cannot be projected onto a screen. |
| Location (Mirrors) | Always on the same side as the object (in front of the mirror). | Always on the opposite side of the mirror (behind the mirror). |
| Location (Lenses) | Always on the opposite side of the lens from the object. | Always on the same side of the lens as the object. |
| Example | Image on a movie screen, image formed by a projector lens. | Your reflection in a plane mirror, image through a magnifying glass. |
A real image is formed when light rays pass through and diverge from the image point, meaning the light energy actually converges at that location. For virtual images, the brain perceives an image at a point where light rays merely appear to originate, even though no light physically converges there.
Practical Applications and Insights
- Magnifying Glass (Converging Lens): When an object is placed within the focal length of a converging lens, the rays from the object diverge after passing through the lens. Extending these diverging rays backward reveals a magnified, upright, and virtual image. This is why a magnifying glass makes objects appear larger without actually converging light to a point you could project.
- Projectors (Converging Lens): In a projector, a real, inverted, and magnified image is formed on a screen. This occurs because the object (e.g., a slide or digital display) is placed just beyond the focal point of the projection lens, causing light rays to converge and form a real image that can be seen on the screen.
- Plane Mirrors: When you look into a plane mirror, your reflection is a virtual image. The light rays diverging from your body hit the mirror and reflect. Your brain interprets these reflected rays as coming from a point behind the mirror, even though no light actually passes behind it.
By meticulously following the path of light rays, particularly the principal rays, we can precisely determine the characteristics and location of an image formed by any optical system, whether it's a simple mirror or a complex lens array.
