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Optics Simulator

Thin Lens Formula & Ray Diagram Simulator

Adjust focal length, object distance, and height to visualize image formation with 3 principal rays in real time. Image distance, magnification, and image type calculated automatically.

Parameters
Lens Type
Focal length f 100 mm
Convex: f > 0   Concave: f < 0 (set automatically)
Object distance u 200 mm
Object height h 20 mm
Sign convention: object distance u is negative (u = −|u|). Image distance v > 0 → real image; v < 0 → virtual image.
200.0
Image distance v [mm]
−1.00
Magnification m
Real
Image type
Inverted
Orientation / Size

Theory

Thin lens formula (Gaussian form, sign convention):

$$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$$

Magnification: $m = \dfrac{v}{u}$   ($m < 0$: inverted, $|m| > 1$: enlarged)

Object distance is negative ($u = -|u_{\rm obj}|$); real image: $v > 0$; virtual image: $v < 0$

Convex lens: $f > 0$    Concave lens: $f < 0$

Engineering applications: Industrial camera working distance and magnification design / Microscope and telescope optical system layout / Laser beam expanders / Optical displacement sensor focus design / Initial layout verification in CAE optical simulation (Zemax OpticsStudio).