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.
Key Formula
1/f = 1/v - 1/u (using sign convention: real-is-positive for v, virtual-is-negative for u)
LaTeX: \frac{1}{f} = \frac{1}{v} - \frac{1}{u}
| Symbol | Meaning | Unit |
|---|---|---|
| f | Focal length of the lens | metres (m) |
| v | Image distance from optical centre | metres (m) |
| u | Object distance from optical centre (negative if real) | metres (m) |
Worked Example
Problem
An object is placed 30 cm from a convex lens of focal length 10 cm. Find the image distance.
Solution
Step 1: Use the lens formula: 1/f = 1/v − 1/u Step 2: Using sign convention (object on left, distances measured from lens): u = −30 cm, f = +10 cm Step 3: 1/v = 1/f + 1/u = 1/10 + 1/(−30) = 3/30 − 1/30 = 2/30 Step 4: v = 30/2 = +15 cm
Answer
Image forms 15 cm to the right of the lens (real and inverted)
Comparison of Convex and Concave Lenses
| Property | Convex (Converging) | Concave (Diverging) | Unit |
|---|---|---|---|
| Shape | Thicker at centre | Thinner at centre | — |
| Focal length sign | Positive (+f) | Negative (−f) | m |
| Power | Positive | Negative | Dioptre (D) |
| Image type | Real or virtual | Always virtual | — |
| Common use | Magnifying glass, camera | Spectacles for myopia | — |
Interactive Tools
Wikimedia Commons, CC BY-SA
Related Terms
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.
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).
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.
From Latin "lens" (genitive "lentis") meaning "lentil", because early glass lenses were shaped like the lentil seed. The optical use of the term dates to the 17th century. Roger Bacon described lenses for magnification around 1268, and ground lenses were used in spectacles by 1300 CE in Italy.