1. What a lens does to light
A lens is a transparent piece of glass or plastic that bends light in a controlled way. Because light slows down inside a lens and travels faster outside, the curved surfaces make the rays either come together (converge) or spread apart (diverge).
This bending of light is what lets lenses form images, magnify objects and focus beams.
2. Types of lenses
Lenses are usually classified based on their shapes. I think of them in two main categories:
2.1. Convex (converging) lens
A convex lens is thicker at the centre and thinner at the edges. It bends parallel rays so that they meet at a point on the other side. This point is called the principal focus.
Convex lenses can form real or virtual images depending on where the object is placed.
2.2. Concave (diverging) lens
A concave lens is thinner at the centre and thicker at the edges. It spreads out parallel rays so that they appear to come from a point behind the lens. This point is its virtual focus.
Concave lenses always form virtual, upright and smaller images.
3. Basic terms used with lenses
When working with lens diagrams, I use a standard set of terms:
- Principal axis: A straight line passing through the centre of the lens.
- Optical centre (O): A central point where a ray passes straight without bending.
- Principal focus (F): The point where parallel rays converge (convex) or appear to diverge from (concave).
- Focal length (f): The distance between O and F.
- Aperture: The region of the lens through which light can pass.
4. Sign convention for lenses
The same sign convention used for mirrors is followed here:
- Distances measured opposite to incoming light → negative.
- Distances measured in the direction of incoming light → positive.
- Convex lens focal length is positive.
- Concave lens focal length is negative.
- Heights above the principal axis → positive; below → negative.
5. How a convex lens bends light
A convex lens brings parallel rays to a point. This is why it is called a converging lens. The bending comes from the curved surfaces — each surface refracts the ray according to Snell’s law.
5.1. Parallel rays meeting at the focus
When a set of parallel rays enters a convex lens, they bend toward the principal axis and meet at the focal point on the other side. This is useful for focusing light in cameras, magnifiers and projectors.
6. How a concave lens bends light
A concave lens spreads out parallel rays. The rays diverge in such a way that, when extended backward, they seem to come from a single point on the same side of the lens. This is why it is called a diverging lens.
6.1. Virtual focus
The point from which the diverged rays appear to come is called the virtual focus. Unlike a convex lens, a concave lens never produces a real focus for parallel rays.
7. Ray diagrams I usually draw for lenses
To find where the image forms, I usually draw two principal rays:
- A ray parallel to the principal axis (passes through F for convex; appears to come from F for concave).
- A ray passing through the optical centre (goes straight without bending).
- For convex lenses: a ray passing through F emerges parallel.
Two rays are enough to locate the image clearly.
8. Image formation: how it changes with object position
Convex and concave lenses behave quite differently. Here’s a quick summary of how images change:
8.1. For a convex lens
- Object far away: Real, inverted, small.
- At 2F: Real, inverted, same size.
- Between F and 2F: Real, inverted, magnified.
- At F: Image at infinity.
- Between O and F: Virtual, upright, magnified.
8.2. For a concave lens
- Always forms a virtual image.
- Always upright and smaller.
- Image forms between O and F.
9. A simple example
If parallel rays enter a convex lens of focal length \(f = 15\, \text{cm}\), they will converge at a point 15 cm away from the optical centre. If the same rays enter a concave lens of focal length \(-15\, \text{cm}\), they will diverge as if they were coming from a point 15 cm behind the lens.
10. Where I see lenses being used
Lenses are everywhere in optical devices:
- Magnifying glasses.
- Eyeglasses (convex for hypermetropia and concave for myopia).
- Cameras and projectors.
- Microscopes and telescopes.
Understanding how they bend light makes these devices much easier to understand.