Convex Lens
A convex lens (also called a converging lens) is an optical element that is thicker at its centre than at its edges, causing parallel rays of light passing through it to converge toward a single real focal point on the far side. The converging power arises from refraction at both curved surfaces, and the focal length is positive. Convex lenses are used in magnifying glasses, cameras, projectors, the human eye's cornea and crystalline lens, and corrective spectacles for hyperopia (long-sightedness).
Key Formula
1/f = 1/v + 1/u (Cartesian sign convention: object distance u is negative for real object)
LaTeX: \frac{1}{f} = \frac{1}{v} + \frac{1}{u}
| Symbol | Meaning | Unit |
|---|---|---|
| f | Focal length (positive for convex lens) | cm or m |
| v | Image distance from lens | cm or m |
| u | Object distance from lens | cm or m |
Worked Example
Problem
An object 4 cm tall stands 20 cm in front of a convex lens of focal length 15 cm. Find the image distance and image height using the Cartesian convention (u = −20 cm).
Solution
Step 1: Lens formula (Cartesian): 1/v − 1/u = 1/f Step 2: 1/v − 1/(−20) = 1/15 → 1/v + 1/20 = 1/15 Step 3: 1/v = 1/15 − 1/20 = 4/60 − 3/60 = 1/60 → v = 60 cm Step 4: Magnification m = v/u = 60/(−20) = −3 (inverted) Step 5: Image height = m × object height = −3 × 4 = −12 cm
Answer
Image forms 60 cm beyond the lens; image height = 12 cm (real, inverted, magnified 3×)
Image Formation by a Convex Lens at Different Object Positions
| Object Position | Image Position | Nature | Size |
|---|---|---|---|
| Beyond 2F | Between F and 2F | Real, inverted | Diminished |
| At 2F | At 2F (other side) | Real, inverted | Same size |
| Between F and 2F | Beyond 2F | Real, inverted | Magnified |
| At F | At infinity | Real, inverted | Infinitely large |
| Between F and lens | Same side as object | Virtual, upright | Magnified |
Interactive Tools
PhET Geometric Optics
Move an object to different positions relative to a convex lens and observe all image cases.
Open ToolGeoGebra Convex Lens Ray Diagram
Draw and interact with principal-ray diagrams for a converging lens.
Open ToolKhan Academy – Converging Lenses
Video walkthrough of image formation cases for converging lenses.
Open Tool
Wikimedia Commons, CC BY-SA
Related Terms
Concave Lens
A concave lens (also called a diverging lens) is an optical element that is thinner at its centre than at its edges, causing parallel rays of light passing through it to spread apart as if they originated from a virtual focal point on the same side as the incoming light. The focal length is negative, and the lens always produces a virtual, upright, and diminished image regardless of object position. Concave lenses are used to correct myopia (short-sightedness), in Galilean telescopes, and in laser beam expanders.
Focal Length
Focal length (f) is the distance from the optical centre of a lens or curved mirror to its principal focus — the point where parallel rays of light converge (converging lens/mirror) or appear to diverge from (diverging lens/mirror) after passing through or reflecting off the optical element. A shorter focal length means stronger light-bending power, quantified as optical power P = 1/f in dioptres. Focal length governs image magnification, field of view, and is central to the design of cameras, telescopes, and corrective eyewear.
Lens (Optics)
In optics, a lens is a transmissive optical element, typically made of glass or transparent plastic, that refracts light to converge or diverge rays, thereby forming images. Lenses work by exploiting the refraction of light at curved surfaces, and their shape (convex or concave) determines whether rays are brought together (converging) or spread apart (diverging). Lenses are fundamental components of eyeglasses, cameras, microscopes, telescopes, and the human eye itself.
From Latin "convexus" meaning "arched" or "rounded outward". The term has been used in optics since the 17th century. Galileo Galilei used convex lenses in his 1609 telescope, and they were foundational in the development of microscopy by Antonie van Leeuwenhoek in the 1670s.