👓 Geometric Optics & Focal Mechanics
Thin Lens & Curved Mirror Calculator
Compute image distance ($d_i$), focal length ($f$), and magnification ($M = -d_i/d_o$) for convex converging lenses, concave diverging lenses, and spherical curved mirrors.
🔍 Converging Lens (f = +10 cm, do = 30 cm)
🔎 Magnifying Glass (f = +10 cm, do = 5 cm)
👓 Diverging Lens (f = -15 cm, do = 20 cm)
🪞 Concave Mirror at Center (do = 2f)
Optical Parameters
cm
+ = Converging / Convex, - = Diverging / Concave
cm
cm
Image Distance (d_i)
15.00 cm
Magnification ($M$)
-0.500×
Image Height ($h_i$)
-2.50 cm
Optical Power ($D$)
+10.00 D
💡 Gaussian Lens Formula:
$$\frac{1}{d_i} = \frac{1}{f} - \frac{1}{d_o} = \frac{1}{10.0} - \frac{1}{30.0} = \frac{2}{30} \implies d_i = 15.0\text{ cm}$$
The Gaussian Lens & Mirror Equation
For paraxial light rays through thin lenses and curved mirrors:
$$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \iff d_i = \frac{f \cdot d_o}{d_o - f}$$
- Magnification: $$M = -\frac{d_i}{d_o} = \frac{h_i}{h_o}$$
- Real vs Virtual: $d_i > 0$ denotes a real image formed by converging rays; $d_i < 0$ denotes a virtual image on the same side as the object.
- Optical Power ($P$ in Diopters): $D = \frac{1}{f_{\text{meters}}}$.