Water Drop Lens
A water droplet sitting on a surface acts as a tiny converging lens. Light rays entering from above are refracted by the curved water-air interface according to Snell’s law. The curvature of the drop determines the focal length — smaller, more curved drops focus light more strongly.
n1 sin θ1 = n2 sin θ2 | f = R / (2(n − 1))
Droplets as lenses
When a water droplet sits on a flat surface, it forms a curved dome due to surface tension. This curved interface between water (n ≈ 1.33) and air (n ≈ 1.00) refracts light just like a glass lens. The smaller and more curved the droplet, the shorter the focal length and the more powerfully it focuses light. This is why you can sometimes see tiny inverted images through water drops on a leaf.
Snell’s law at curved surfaces
At each point on the curved surface, the normal direction is different. A parallel beam of light hits the surface at varying angles of incidence across its width. Applying Snell’s law n₁ sin θ₁ = n₂ sin θ₂ at each point, the refracted rays converge toward a focal point. For a spherical surface, the paraxial (thin lens) approximation gives f = R / (n − 1) for a single refracting surface, where R is the radius of curvature.
Convex vs. concave
A normal water drop is convex — it bulges outward and acts as a converging lens. A concave meniscus (like water clinging to the inside of a tube) curves inward and acts as a diverging lens. In the concave case, the refracted rays spread apart, and the focal point is virtual — it appears to be behind the lens rather than in front of it.
Chromatic aberration
Real lenses exhibit chromatic aberration because the refractive index varies slightly with wavelength. Blue light bends more than red, so the focal point for blue is slightly closer to the lens. This simulation’s “Chromatic” mode shows this effect by tracing rays at three wavelengths with slightly different refractive indices.
Spherical aberration
Rays far from the optical axis focus at a slightly different point than paraxial rays. This spherical aberration is visible in the simulation when you increase the curvature — the outer rays converge before the inner rays, creating a caustic pattern rather than a perfect focal point.