Grade 12th passMechanics

Why refractive index is considered as a tensor quantity?

Ishan karki

8 Years agoGrade 12th pass

2 Answers

Arun

Approved Tutor Answer8 Years ago

Physical quantities that vary in two different directions are properly described as tensors. I like to visualize tensors as the surface of a cube (similar to visualizing a vector as an arrow): each face of the cube has 3 directions associated with it- one normal, and two tangential. If you like, you can think of a 2nd-rank tensor as a 'bivector': one vector represents the orientation of a surface (or direction of observation) and the other direction is the direction of a force acting on the surface (or field within the material). Physical properties that are (second rank) tensors include the stress tensor, strain tensor, and the index of refraction of inhomogeneous materials. There are 4th-rank tensors as well: these occur in acousto-optics, mostly- the acoustic field is a 2nd-rank tensor and the refractive index is also a 2nd rank tensor, so relating the two requires a 4th rank tensor.

Miftachul Hadi

7 Years ago

Actually, every physical quantity should be able to be expressed in tensor.

As we know, scalar is a tensor rank 0, vector is a tensor rank 1, and so on .. .

Refractive index, n, can be defined as n = \sqrt{\varepsilon_r \mu_r} where \varepsilon = 1 + \chi_e and \mu_r = 1 + \chi_m, \chi_e and \chi_m are electric suceptibilty and magnetic suceptibilty respectively. In anisotopic medium, both, \chi_e and \chi_m are expressed as a tensor.

CMIIW.

Thank you.

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