Geometrical Optics: Lenses & Mirrors Simulator

Programmed by Eidan A. Abdullah – Optics Course, College of Science, Wasit University - Iraq

DOI: 10.5281/zenodo.18070606 · GitHub repository ⭐ (support the project)

Lens Type & Sign Convention

Convex (+f)

Concave (−f)

Thin-Lens Equation:

1/f = 1/s + 1/s′

f > 0 convex, f < 0 concave
s > 0 object on the left (real object)
s < 0 object on the right (virtual object on image side)
s′ > 0 real image (right), s′ < 0 virtual (left)

Object & Lens Parameters

Focal length |f| (cm) 15.00 cm

Object distance s (cm) 30.00 cm

Positive: object on the left of the lens (real object).
Negative: object on the right of the lens (virtual object, s < 0).

Object height y (cm) 10.00 cm

Rays & Examples

Image distance s′ –

Image height y′ –

Magnification M –

Nature –

Position –

Adjust parameters to see how the sign of s and s′ controls the nature of the image.

Lens 1 & Lens 2 Types

Lens 1: Convex

Lens 1: Concave

Lens 2: Convex

Lens 2: Concave

Two-Lens System

Lens 1: 1/f₁ = 1/s₁ + 1/s₁′
Lens 2: 1/f₂ = 1/s₂ + 1/s₂′
s₂ = d − s₁′ (with signs!)
Total magnification M = M₁ · M₂

Parameters

|f₁| (cm)

|f₂| (cm)

Object distance s₁ (cm)

s₁ < 0 ⇒ virtual object for lens 1 (on right side).

Lens separation d (cm)

Object height y (cm)

s₁′ –

s₂ –

s₂′ –

Total M –

Final y₂′ –

Lens 1 forms an intermediate image that acts as the object for Lens 2. The signs of s₁′ and s₂ are crucial.

Section 3: Lens Maker's Formula

Refractive index n 1.52

Enter refractive index value directly.

Front radius R₁ (cm) +15.0

Positive → convex toward object. Negative → concave.

Back radius R₂ (cm) +5.0

Positive → convex toward image. Negative → concave.

Lens Maker’s Formula:

1/f = (n − 1) (1/R₁ − 1/R₂)

R₁, R₂ in meters
Plano: |R| → ∞ → 1/R = 0
Optical power P = 1/f

Focal length f –

Optical power P –

Lens type –

R₁ (cm) –

R₂ (cm) –

Move n, R₁ and R₂. The program uses the exact Lens Maker's formula and draws each spherical surface from its radius. Very large |R| (> 300 cm) is treated as plano (flat surface). Centers of curvature C₁ and C₂ are marked to make the sign convention visually clear.

Mirror Type & Sign Convention

Concave Mirror (+f)

Convex Mirror (−f)

Spherical Mirror Equation:

1/f = 1/s + 1/s′

f > 0 concave mirror, f < 0 convex mirror
s > 0 real object (in front of mirror)
s < 0 virtual object (behind mirror)
s′ > 0 real image (in front of mirror)
s′ < 0 virtual image (behind mirror)

Object & Mirror Parameters

Radius of curvature |R| (cm) 15.00 cm