Concave Lens Calculator
Calculate the focal length of diverging lenses including biconcave and plano-concave types. Essential for myopia correction and optical design.
Use Calculator Now ↓Lens Maker Formula
1/f = (n-1)(1/R₁ - 1/R₂)
Common: Crown glass (1.52), Flint glass (1.62), Plastic (1.49)
Concave surface: negative value
For biconcave: positive value
What is a Concave Lens?
A concave lens (also called a diverging lens or negative lens) is thinner at the center than at the edges. When parallel light rays pass through a concave lens, they spread apart and appear to diverge from a virtual focal point on the same side of the lens as the light source.
Biconcave Lens
Both surfaces curve inward. Most common diverging lens type. R₁ < 0, R₂ > 0
Plano-Concave Lens
One flat surface, one concave surface. One R = ∞ (flat side)
Negative Meniscus
Both surfaces curve the same way, but the concave side curves more. Still diverging overall.
Why is Concave Lens Focal Length Negative?
Concave lenses have negative focal length because they create a virtual focal point. Unlike convex lenses that converge light to a real point, concave lenses diverge light rays. When traced backward, these diverging rays appear to originate from a point on the same side of the lens as the incoming light.
Sign Convention for Biconcave Lens
- R₁ (first surface): Negative (−) - The center of curvature is to the left of the surface (concave facing left)
- R₂ (second surface): Positive (+) - The center of curvature is to the right of the surface (concave facing right)
- Result: f < 0 (negative focal length = diverging lens)
Example Calculation
Given: n = 1.5, R₁ = -10 cm, R₂ = +10 cm
1/f = (1.5 - 1)(1/(-0.10) - 1/0.10)
1/f = 0.5 × (-10 - 10) = 0.5 × (-20) = -10
f = -0.1 m = -10 cm (diverging)
Applications of Concave Lenses
Myopia Correction
Concave lenses in eyeglasses diverge light before it enters the eye, correcting nearsightedness by moving the focal point back onto the retina.
Galilean Telescopes
The eyepiece of a Galilean telescope is a concave lens, producing an upright image (unlike Keplerian telescopes with convex eyepieces).
Door Peepholes
Wide-angle peepholes use concave lenses to provide a broad field of view while making approaching visitors appear smaller.
Laser Beam Expanders
Concave lenses diverge laser beams before they pass through a convex lens, creating expanded, collimated beams.
Camera Viewfinders
Some camera viewfinders use concave lenses to help nearsighted photographers see the image clearly without glasses.
Aberration Correction
Concave elements in compound lenses help correct chromatic and spherical aberrations caused by convex elements.
Frequently Asked Questions
What is a concave lens?
A concave lens is a diverging lens that is thinner in the middle than at the edges. It spreads parallel light rays apart so they appear to come from a virtual focal point. Common types include biconcave (curved inward on both sides) and plano-concave (one flat side). Concave lenses always have negative focal length.
Why is the focal length of a concave lens negative?
Concave lenses diverge light rays instead of converging them. The focal point is virtual - it is where the diverging rays appear to originate from when traced backward. By convention, virtual focal points have negative focal length, distinguishing diverging lenses from converging (positive) lenses.
How do concave lenses correct myopia (nearsightedness)?
In myopia, the eye focuses images in front of the retina. A concave lens diverges incoming light rays, effectively moving the focal point backward onto the retina. The required lens power (in negative diopters) depends on how nearsighted the person is.
What is the difference between concave and convex lenses?
Convex lenses are thicker in the middle, converge light to a real focal point, and have positive focal length. Concave lenses are thinner in the middle, diverge light from a virtual focal point, and have negative focal length. Convex lenses magnify; concave lenses minify.
Can a concave lens form a real image?
No, a single concave lens cannot form a real image. It always produces virtual, upright, and reduced images regardless of object distance. Real images require light rays to actually converge, which diverging lenses cannot do alone. However, concave lenses can contribute to real image formation when combined with convex elements in compound lens systems.