See a force. The hidden stress.

Real principles. A deliberately simple specimen.

This is an ideal, initially unstressed, transparent elastic beam. The rendered apparatus is an illustration, not a measured instrument or specimen. Span 80 mm; vertical depth 8 mm; light-path thickness 2–5 mm. The supports allow rotation. The force acts vertically at 20–80% of the span.

Young’s modulus E = 2.3 GPa and stress-optic coefficient C = 60 × 10⁻¹² Pa⁻¹ are chosen teaching values for a polymer-like material, not calibrated material data. We use small-deflection Euler–Bernoulli beam theory. I = t h³ / 12; σₓ = −My/I. Bending stress is treated as constant along the light path; optical retardation Γ = C |σₓ| t.

The bending-only approximation omits shear-induced birefringence, local loading and support contact stresses, residual manufacturing stress, plastic deformation, creep, absorption and wavelength dependence of the material coefficient. Do not use the contact regions for engineering interpretation. The beam rebounds because it is ideal elastic; real plastic can retain stress or deform permanently. The shape uses calculated deflection without an exaggeration factor.

The rear polarizer’s transmission axis is 45° to the beam. The front analyzer’s angle is relative to that axis. With crossed axes, I / I₁ = sin²(πΓ/λ), where I₁ is the intensity after the first polarizer. Other angles use the equivalent Jones-retarder calculation. Crossed refers to the transmission axes, not perpendicular glass panels. Ordinary-light and polarized-light views are normalized separately; the wipe is a comparison, not a partly inserted physical filter.

Colour integrates 380–780 nm in 5 nm steps under D65 illumination using approximate CIE 1931 matching functions, then converts to sRGB with out-of-gamut clipping. The displayed field uses an interpolated retardation lookup table. Higher-order white-light fringes can become pale. The specimen colour is calculated for normal incidence even in the assembly view; camera perspective does not recalculate optical path length. Only the strip's front face displays the calculated transmission. The empty aperture follows the same analyzer transmission. The ordinary-light wipe removes filter effects for comparison while the illustrated filter holders stay mounted. The Higgsfield-authored apparatus is shaded to illustrate its construction; it is not a scanned or measured instrument.

Thickness has two linked roles. At fixed load, increasing t reduces bending stress as 1/t but increases the optical path as t. Thus Γ is unchanged in this uniform beam model, even though deflection and stress fall. A particular colour does not uniquely identify stress, its sign, or damage. The same retardation can occur in tension and compression.

• Nikon MicroscopyU · Principles of birefringence
• Daniel Post · Photoelasticity, Society for Experimental Mechanics (PDF)
• MIT OpenCourseWare · Mechanics & Materials I, beam bending
• CIE · D65 standard illuminant dataset
• Wyman, Sloan & Shirley (2013) · Analytic CIE colour-matching approximations

D65 data is reused from MVLscope’s spectral model, under CC BY-SA 4.0; data attribution and modifications. References support principles; they do not endorse this exhibit.