iGOLab — Interactive Geometrical Optics Laboratory

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

Ray display Choose the construction rays

Quick examples Load a standard optical case

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) +20.0

Positive → convex toward object. Negative → concave.

Back radius R₂ (cm) -20.0

Positive → convex toward image. Negative → concave.

Lens Maker’s Formula:

1/f = (n − 1) (1/R₁ − 1/R₂)

R₁ and R₂ are entered in cm and converted internally
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 standard thin-lens Lens Maker's relation in air 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

Object distance s (cm) 30.00 cm

Positive: object in front of the mirror (real object).
Negative: object behind the mirror (virtual object, s < 0).

Object height y (cm) 10.00 cm

Ray display Choose the principal construction rays

Image distance s′ –

Image height y′ –

Magnification M –

Nature –

Position –

Adjust parameters to explore image formation in spherical mirrors.

Thick Lens: Paraxial Matrix Method

Reduced-ray matrix: [y, nθ]ᵀ

M = S₂ · T(t,n) · S₁ = [A B; C D]

EFL = −n₀/C

Light travels from left to right.
R > 0: center of curvature is to the right of the surface vertex.
R = 0 is treated as a plano surface.
All distances are measured from the two surface vertices unless stated otherwise.
Fixed physical drawing scale: changing object distance, object height, refractive index, focal length, or image position never resizes the lens.

Lens & Object Parameters

External index n₀ 1.00

Lens index n 1.52

Front radius R₁ (cm) +20.0

Back radius R₂ (cm) −20.0

Central thickness t (cm) 4.00

Semi-aperture a (cm) 8.00

Object distance s (cm) 30.0

Object height y (cm) 6.00

Examples

Principal planes & focal points Three paraxial rays Centers of curvature

Publication export: high resolution, synchronized dimensions, and enlarged labels.

Equivalent focal length (EFL)–

Equivalent power–

Front focal point from V₁–

Back focal length from V₂–

H₁ from V₁–

H₂ from V₂–

Image distance q from V₂–

Image height y′–

Magnification m–

Image nature–

Thin-lens EFL–

Thickness effect on EFL–

This module uses standard first-order (paraxial) thick-lens optics. The two refracting surfaces and translation through the lens are treated separately.

Prism Refraction and Deviation

Prism and incident-ray parameters

Apex angle A (°) 60.0

Prism index n 1.500

External-medium index n₀ 1.000

Incidence angle i₁ (°) 48.59

Angles are measured from the normal. The prism is homogeneous and the surrounding medium is the same at both faces.

Normals Angle labels Deviation reference

Relations used
n₀ sin(i₁) = n sin(r₁)
r₁ + r₂ = A
n sin(r₂) = n₀ sin(e)
δ = i₁ + e − A

Parallel-sided slab parameters

Slab thickness t (cm) 8.00

Slab index n 1.500

External-medium index n₀ 1.000

Incidence angle i (°) 45.00

The slab faces are parallel and the same external medium surrounds both sides. Therefore, whenever transmission occurs, the emergent ray is parallel to the incident ray.

Normals Angle labels Original path Lateral shift

Relations used
n₀ sin(i) = n sin(r)
e = i
d = t sin(i − r) / cos(r)

The displayed displacement d is the shortest distance between the emergent ray and the undeviated continuation of the incident ray.

First refraction r₁–
Second incidence r₂–
Emergence angle e–
Total deviation δ–
Minimum-deviation incidence–
Minimum deviation δmin–
Critical angle θc–
Relative index n/n₀–
Small-angle estimate–
Optical path–

Refraction angle r–
Emergence angle e–
Lateral displacement d–
Internal path length–
Optical path in slab–
Critical angle θc–
Relative index n/n₀–
Ray status–

                            Adjust the apex angle, refractive indices, or incidence angle to explore refraction and angular deviation through a prism.
                        

Interactive Optical Bench – Drag, Trace & Measure v21.9 Project Import/Export + Photodetector

Ready optical system

Add optical element

⚙ Bench

Camera — object, diaphragm, converging lens, and image sensor.

Choose an example or add an optical element. 1 major grid = 5 cm

Optical elements0

Traced rays (max 14)0

Interactions0

Screen hits0

Mean screen coordinate–

Screen RMS spread–

Active detector–

Detected power–

Relative power–

Focus signal–