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.
Key Formula
m = v/u (magnification, where v and u follow Cartesian sign convention)
LaTeX: m = \frac{v}{u} = \frac{f}{f + u}
| Symbol | Meaning | Unit |
|---|---|---|
| m | Linear magnification | dimensionless |
| v | Image distance (negative for virtual image on same side as object) | m |
| u | Object distance (negative for real object) | m |
| f | Focal length (negative for concave/diverging lens) | m |
Worked Example
Problem
An object is placed 30 cm in front of a concave lens of focal length −10 cm. Find the image distance and magnification.
Solution
Step 1: Lens formula (Cartesian): 1/v − 1/u = 1/f Step 2: u = −30 cm, f = −10 cm Step 3: 1/v = 1/f + 1/u = 1/(−10) + 1/(−30) = −3/30 − 1/30 = −4/30 Step 4: v = −30/4 = −7.5 cm (negative → virtual image on same side as object) Step 5: m = v/u = (−7.5)/(−30) = +0.25
Answer
Image forms 7.5 cm in front of the lens (virtual, upright); magnification = 0.25 (image is ¼ object size)
Comparison: Concave Lens vs. Convex Lens Image Properties
| Property | Concave (Diverging) | Convex (Converging) |
|---|---|---|
| Focal length sign | Negative (−f) | Positive (+f) |
| Image nature | Always virtual | Real or virtual |
| Image orientation | Always upright | Upright (virtual) / Inverted (real) |
| Image size | Always diminished | Same / magnified / diminished |
| Vision correction | Myopia (−D prescription) | Hyperopia (+D prescription) |
| Optical power | Negative | Positive |
Interactive Tools
Wikimedia Commons, CC BY-SA
Related Terms
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).
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 "concavus" meaning "hollow" or "vaulted inward" (con- = together/thoroughly, cavus = hollow). The optical use of "concave" dates to the 14th century in Latin texts and appeared in English by the 15th century. Concave lenses were used in Galileo's telescope (1609) as the eyepiece.