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Thermodynamics

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Fresnel Rhomb

Fresnel constructed rhomb of glass whose angles are 54˚ and 126˚ as shown in fig. based upon the fact that a phase difference of π/4 is introduced between the component vibrations (parallel and perpendicular to the plane of incidence) when light is totally internally reflected back at glass-air interface when the angle of incidence is 54˚.

A ray of light enters normally at one end of the rhomb and is totally internally reflected at the point B along BC. The angle of incidence at B is 54˚, which is more than the critical angle of glass. Let the incident light be plane polarized, and let the vibrations make an angle of 45˚ with the plane of incidence. Its components (i) parallel to the plane of incidence and (ii) perpendicular to the plane of incidence are equal. These components after reflection at the point B undergo a phase difference of π/4 or a path difference of λ/8. A further phase difference of π/4 or a path difference of λ/8 is introduced between the components when the ray BC is totally internally reflected back along CD. Therefore the final emergent ray DE has two components vibrating at right angles to each other and they have a path difference of λ/4. Therefore the emergent light DE is circularly polarized. Fresnel’s rhomb works similar to a quartz wave plate.

If the light entering the Fresnel’s rhomb is circularly polarized, a further path difference of λ/4 is introduced between the component vibrations. The total path difference between the component vibrations is λ/2. Therefore the emergent light is plane polarized and its vibrations make an angle of 45˚ with the plane of incidence.

When an elliptically polarized light is passed through a Fresnel’s rhomb, a further path difference of λ/4 is introduced between the component vibrations (parallel and perpendicular to the plane of incidence). The total path difference between the component vibrations is λ/2 and the emergent light is plane polarized.

Thus, Fresnel’s rhomb behaves just similar to a quarter wave plate. A quarter wave plate is used only for light of a particular wavelength, whereas a Fresnel’s rhomb can be used for light of all wavelengths.