# Stress-Optic Law

## Description

Photoelasticity is an experimental method to determine the stress distribution in a material.Unlike the analytical methods of stress determination, photoelasticity gives a fairly accurate picture of stress distribution, even around abrupt discontinuities in a material. The method is an important tool for determining critical stress points in a material, and is used for determining stress concentration in irregular geometries.

When a ray of light passes through a photoelastic material, its electromagnetic wave components gets resolved along the two principal stress directions and each of these components experiences different refractive indices due to the birefringence. The difference in the refractive indices leads to a relative phase retardation between the two components. Assuming a thin specimen made of isotropic materials, where two-dimensional photoelasticity is applicable. The magnitude of the relative retardation is given by the stress-optic law

## Variables

Δ | induced retardation (dimensionless) |

π | pi |

t | specimen thickness (m) |

λ | wavelength (m) |

C | stress-optic coefficient (m^{2}/N) |

σ_{1} | first principal stress (N/m^{2}) |

σ_{2} | second principal stress (N/m^{2}) |