With a convex lens (a lens that bulges outward, thicker in the middle), magnification works through refraction and the geometry of ray diagrams. Here’s how it breaks down:
- The Basic Principle: Refraction
A convex lens bends light rays inward (converging them). Parallel rays entering the lens all meet at a single point called the focal point (F). The distance from the lens to this point is the focal length (f).
- The Thin Lens Equation
This governs where an image forms:
1/f = 1/dₒ + 1/dᵢ
· f = focal length
· dₒ = object distance (from lens to object)
· dᵢ = image distance (from lens to image)
- The Magnification Formula
Magnification (M) tells you how much bigger or smaller the image is compared to the object:
M = -dᵢ / dₒ = hᵢ / hₒ
· hᵢ = image height
· hₒ = object height
· The negative sign means the image is inverted (upside down)
- How Magnification Changes with Object Distance
This is the key insight. As you move the object closer to the lens, magnification increases:
Object Position Image Type Magnification
Far away (dₒ > 2f) Real, inverted, smaller M < 1 (reduced) At 2f (dₒ = 2f) Real, inverted, same size M = 1 Between f and 2f Real, inverted, larger M > 1
At f (dₒ = f) No image formed Infinite (rays parallel)
Inside f (dₒ < f) Virtual, upright, larger M > 1 (magnifying glass)
- Ray Diagram: How It Actually Works
Three principal rays show where the image forms:
- Ray parallel to axis → refracts through the focal point on the other side
- Ray through the center → passes straight through undeviated
- Ray through the near focal point → emerges parallel to the axis
Where these rays intersect is where the image forms. The farther the intersection is from the axis, the larger the magnification.
- The Magnifying Glass Case (Most Common)
When you hold a convex lens closer than f to an object:
· The rays diverge after passing through the lens
· Your eye traces them backward to form a virtual image
· This virtual image is upright and larger
· M = 1 + (25cm / f) for a relaxed eye (25cm = near point of human vision)
Example: A lens with f = 5cm gives M = 1 + 25/5 = 6× magnification
- Why Convex Lenses Magnify (Intuition)
Think of it this way:
· A convex lens compresses the angle of incoming light rays
· Your eye receives rays that appear to come from a larger object farther away
· The brain interprets this as a bigger object
· The closer the object is to the focal point, the more extreme this effect becomes
- Real vs. Virtual Images
· Real image (dₒ > f): Can be projected on a screen. Inverted. Used in cameras, projectors.
· Virtual image (dₒ < f): Cannot be projected. Upright. Used in magnifying glasses, eyeglasses.
Summary
A convex lens magnifies by refracting light to converge rays, forming an image whose size depends on the ratio of image distance to object distance. Move the object closer to the focal point → magnification increases. Inside the focal point → you get an upright virtual image (magnifying glass). Beyond it → you get an inverted real image (camera/projector).