Thin Lens Equation

Interactive simulation — adjust parameters and watch the visualization update in real time.

Live graphs

How it works

The Gaussian thin-lens formula relates object distance, image distance, and focal length. The graph of d_i versus d_o is a hyperbola with a vertical asymptote at d_o = f for a converging lens. Moving the pink point with the d_o slider shows how small changes near the focal plane send the image to infinity or flip the sign of d_i.

Key equations

1/f = 1/d_o + 1/d_i
d_i = d_o f / (d_o − f)  ·  m = −d_i/d_o