Convex Lens Calculator
Calculate the focal length of converging lenses including biconvex and plano-convex types. Perfect for magnifying glasses, camera lenses, 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)
Convex surface: positive value
For biconvex: negative value
What is a Convex Lens?
A convex lens (also called a converging lens or positive lens) is thicker at the center than at the edges. When parallel light rays pass through a convex lens, they bend inward and converge at a focal point on the opposite side of the lens.
Biconvex Lens
Both surfaces curve outward. Most common type of convex lens. R₁ > 0, R₂ < 0
Plano-Convex Lens
One flat surface, one convex surface. Used when light enters from the flat side. One R = ∞
Positive Meniscus
Both surfaces curve the same way, but one more than the other. Still converging overall.
Sign Convention for Convex Lenses
Understanding the sign convention is crucial for correctly using the lens maker formula with convex lenses:
For a Biconvex Lens
- R₁ (first surface): Positive (+) - The center of curvature is to the right of the surface (convex facing left)
- R₂ (second surface): Negative (−) - The center of curvature is to the left of the surface (convex facing right)
- Result: f > 0 (positive focal length = converging 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 (converging)
Applications of Convex Lenses
Magnifying Glasses
Simple convex lenses create magnified virtual images of nearby objects.
Camera Lenses
Camera objectives use multiple convex elements to focus real images onto sensors.
Reading Glasses
Convex lenses correct farsightedness (hyperopia) by converging light before it enters the eye.
Microscope Objectives
High-power convex lenses create magnified real images of tiny specimens.
Telescope Objectives
Large convex lenses gather light and create real images of distant objects.
Projectors
Convex lenses project enlarged images from small displays onto screens.
Frequently Asked Questions
What is a convex lens?
A convex lens is a converging lens that is thicker in the middle than at the edges. It bends parallel light rays to meet at a focal point. Common types include biconvex (curved on both sides) and plano-convex (one flat side). Convex lenses always have positive focal length.
How do I calculate the focal length of a convex lens?
Use the lens maker formula: 1/f = (n-1)(1/R₁ - 1/R₂). For a biconvex lens, R₁ is positive and R₂ is negative. For a plano-convex lens, one radius is infinity (flat surface). The result is always a positive focal length for convex lenses.
Why is the focal length of a convex lens positive?
Convex lenses converge light rays to a real focal point on the opposite side of the lens from the light source. By convention, real focal points have positive focal length. This distinguishes them from concave (diverging) lenses which have negative focal length.
What is the difference between biconvex and plano-convex lenses?
A biconvex lens has two curved surfaces (both convex), while a plano-convex lens has one flat surface and one convex surface. Biconvex lenses typically have stronger optical power for the same radii. Plano-convex lenses are often used when light should enter from the flat side to minimize aberrations.
How does refractive index affect a convex lens?
Higher refractive index means stronger light bending at the lens surfaces, resulting in shorter focal length (stronger optical power). A convex lens made from flint glass (n ≈ 1.62) will have a shorter focal length than the same shape made from crown glass (n ≈ 1.52).