In this section we explore how thin converging (convex) lenses and thin diverging (concave) lenses affect a parallel beam of light. Think of a parallel beam like a group of friends walking side‑by‑side. A lens can either bring them together or push them apart.
A thin converging lens has a thicker middle and thinner edges. When a parallel beam strikes it, the rays are bent toward the optical axis and meet at a point called the focal point on the opposite side of the lens. The distance from the lens to this point is the focal length (\$f\$). The lens formula relates the object distance (\$do\$), image distance (\$di\$) and focal length:
\$\frac{1}{f} = \frac{1}{do} + \frac{1}{di}\$
Analogy: Imagine a magnifying glass focusing sunlight to a single spot that can start a fire. The same principle lets a telescope bring distant stars into focus.
A thin diverging lens is thinner in the middle and thicker at the edges. Parallel rays passing through it spread out, as if they had come from a point behind the lens. The apparent point from which the rays seem to diverge is called the virtual focal point, and its distance from the lens is also denoted \$f\$, but it is taken as negative in calculations.
Analogy: Think of a spoon bent outward; light passing through the spoon bends away, just like a crowd of people walking in opposite directions after a split.
Flashlight & Convex Lens: Place a small convex lens in front of a flashlight. The beam becomes a tight spot on a wall, useful for reading or signaling.
Eyeglasses & Diverging Lens: Sunglasses often use concave lenses to spread out light, reducing glare and making the world appear less bright.
Camera Lens: A camera uses a combination of converging lenses to focus light from a scene onto the film or sensor.
| Lens Type | Focal Length (\$f\$) | Image Type |
|---|---|---|
| Converging (Convex) | Positive | Real & inverted (if \$d_o > f\$) |
| Diverging (Concave) | Negative | Virtual & upright |