A raindrop on a window is flat where it touches the glass and curved on the outside — a plano-convex lens. For a thin lens with one flat face, the lensmaker equation reduces to a single curvature term set by Snell's law at the curved surface:
f = R / (n − 1)
where R is the drop's radius of curvature and n its refractive index. The scene behind the glass sits at object distance d₀ from the drop. The thin-lens equation gives the image distance and magnification:
1/d₀ + 1/dᵢ = 1/f
m = −dᵢ / d₀
When d₀ > f the drop forms a real, inverted image (m negative) — this is why a raindrop often shows the world upside-down. When d₀ < f — a small drop close to the background, or a strongly curved drop — the image becomes virtual and upright, magnified like a hand lens (m positive, |m| > 1). Sliding the scene-distance slider across f is exactly what flips the picture inside every drop on screen.
- Refractive index sets how strongly each drop bends light (Snell's law); higher n means a shorter focal length for the same curvature.
- Droplet radius sets R directly, so f = R/(n−1) changes with every slider drag.
- Scene distance is d₀ in the thin-lens equation — the live readout shows exactly where the real/virtual, inverted/upright boundary sits.