Explore the Secrets of Convex Lens Imaging
This interactive simulator helps you visualize the relationship between object distance (u), image distance (v), and focal length (f), and how they affect image properties.
Object Distance (u)
Distance from object to lens
Image Distance (v)
Distance from image to lens
Focal Length (f)
Distance from lens to focal point
Interactive Light Path Simulator
Parameter Controls
Focal length determines lens power; standard magnifying glasses are ~10cm
Distance from object to lens center; drag to adjust
Preset Positions
Display Options
Convex Lens Imaging Principles
Basic Concepts
A convex lens is thicker in the center and thinner at the edges, capable of converging light rays. When parallel light passes through a convex lens, it converges at the focal point (F).
Focal Point (F)
The point where parallel rays converge after passing through the lens
Focal Length (f)
Distance from the lens center to the focal point
Optical Center (O)
Geometric center of the lens; light passes through unchanged
Imaging Laws
The properties of images formed by convex lenses (size, orientation, type) depend on the relationship between object distance (u) and focal length (f).
| Object Distance Range | Image Properties | Applications |
|---|---|---|
| u > 2f | Inverted, reduced, real | Cameras |
| u = 2f | Inverted, same size, real | Focal length measurement |
| f < u < 2f | Inverted, magnified, real | Projectors |
| u = f | No image formed | Parallel light sources |
| u < f | Erect, magnified, virtual | Magnifying glasses |
Lens Formula Derivation
Convex Lens Formula
The relationship between object distance (u), image distance (v), and focal length (f) can be expressed as:
This formula can be derived using similar triangles. When light from an object passes through a convex lens, it forms either a real or virtual image on one side.
Magnification Formula
The ratio of image size to object size is called magnification (m):
When m > 1, the image is larger than the object; when m < 1, the image is smaller.
Derivation Process
1 Similar Triangle Analysis
Consider two rays from the top of the object: one parallel to the principal axis that passes through the focal point after refraction; another that passes through the optical center without changing direction. These rays intersect at the image point.
2 Establishing Proportions
Analyzing the triangles formed by these rays gives the following proportion:
3 Focal Length Relationship
Using another set of similar triangles, we get:
4 Solving the Equations
Combining and simplifying these equations ultimately gives:
Practical Applications
Cameras
Cameras use convex lenses to focus real images of distant objects onto film or image sensors. Object distance (u) is greater than twice the focal length, forming inverted, reduced real images on the image plane.
Projectors
Projectors use convex lenses to project real images of small objects (like slides) onto screens. With object distance between f and 2f, they form inverted, magnified real images on the screen.
Magnifying Glasses
A magnifying glass is a simple convex lens that forms an erect, magnified virtual image when the object distance is less than the focal length (u < f). This virtual image can't be projected but is visible to the eye.