Virtual Labs • Geometrical Optics
Ray Optics Lab
Investigate image formation for mirrors and lenses with draggable objects, dynamic principal ray tracing, and step-by-step formula derivations.
Drag blue arrow horizontally to move object; drag top arrowhead to adjust height.
Object Distance (|u|)
cm
3 cm20 cm40 cm58 cm
Focal Length (|f|)
cm
8 cm15 cm22 cm30 cm
Object Height (hₒ)
cm
2 cm6 cm10 cm16 cm
Display & Annotation Overlays
Live Optical Measurements & Image Properties
Cartesian Sign Convention: Distances in incident direction (right) are positive (+), left are negative (-).
Real ImageInvertedSame Size (1:1)
Object Dist (u)
-30.0 cm
In front (-x)
Image Dist (v)
+30.0 cm
Right side (+x)
Focal Length (f)
+15.0 cm
Converging (Lens) / Div (Mir)
Object Height (hₒ)
+6.0 cm
Upright (+y)
Image Height (hᵢ)
-6.0 cm
Inverted (-y)
Magnification (m)
-1.00×
Real & Inverted
Ray Optics Physical Region & Real-World Application
Object is exactly at 2F (30 cm). The image formed is real, inverted, and the exact same size as the object, located at 2F on the opposite side (magnification m = -1.0). (Used in photocopiers).
Mathematical Derivation & Step-by-Step Substitution
Thin Lens Formula: Connecting the visual ray diagram with the exact formula
Governing Law:Thin Lens Formula
\frac{1}{f} = \frac{1}{v} - \frac{1}{u}
Step-by-Step Numerical Substitution:
1Focal length: f = 15.0 cm
2Object distance: u = -30.0 cm
3Lens formula: 1/f = 1/v - 1/u ⟹ 1/v = 1/f + 1/u
41/v = 1/(15.0) + 1/(-30.0) = 0.0333 cm⁻¹
5Image distance: v = 30.0 cm
6Magnification: m = v/u = (30.0) / (-30.0) = -1.00
7Image height: hᵢ = m × hₒ = (-1.00) × (6.0) = -6.0 cm