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.
Key Formula
P = 1/f
LaTeX: P = \frac{1}{f}
| Symbol | Meaning | Unit |
|---|---|---|
| P | Optical power of the lens | Dioptre (D = m⁻¹) |
| f | Focal length | metres (m) |
Worked Example
Problem
A converging lens has a focal length of 25 cm. What is its optical power in dioptres?
Solution
Step 1: Convert focal length to metres: f = 25 cm = 0.25 m Step 2: Apply power formula: P = 1/f = 1/0.25 Step 3: P = 4.0 D
Answer
Optical power = +4.0 dioptres (positive sign indicates a converging lens)
Focal Length vs. Optical Power and Common Optical Uses
| Focal Length (cm) | Power (D) | Lens Type | Typical Application |
|---|---|---|---|
| 5 | +20 | Strong converging | Microscope objective |
| 25 | +4 | Moderate converging | Reading glasses |
| 50 | +2 | Weak converging | Portrait camera lens |
| −50 | −2 | Weak diverging | Myopia correction −2D |
| −25 | −4 | Moderate diverging | Myopia correction −4D |
Interactive Tools
PhET Geometric Optics
Adjust focal length dynamically and observe changes in image position and size.
Open ToolWolframAlpha – Lens Focal Length
Solve lens equation numerically for any object/image distance and focal length.
Open ToolBrilliant.org – Optics
Conceptual and quantitative treatment of focal length and lens power.
Open Tool
Wikimedia Commons, CC BY-SA
Related Terms
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.
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 "focus" meaning "hearth" or "fireplace" — the burning point of a magnifying glass heated by converging the sun's rays. Johannes Kepler introduced the term "focus" in optics in his 1604 work "Ad Vitellionem Paralipomena". The combined term "focal length" emerged in 18th-century English optical literature.