Interferential devices

The prismatic blade of apex angle of index (figure 8) is lit with almost normal incidence by a monochromatic and extended source.

A part of the incident beam is reflected on the first diopter surface and a second part is refracted in then reflected on the second diopter surface in before it is refracted in . Both beams and stemming from the same incident beam converge in where interfringes are formed. Interferences are located close to the blade, around point . On figure 8, the incidence angle has been considerably incremented, as well as angle for more clarity; in reality angle order of magnitude equals of arc .In almost regular incidence, points and are very close and the blade thickness can locally be considered as constant and equal to . Thus, the difference of optical path between beams and is sensibly equal to the one given by blade with parallel sides placed in the air, lit under normal incidence:

As the corner index is . The reflection in occurs on a more refringent medium than the incident medium when the second reflection in occurs on a less refringent medium than the incident medium of index ; both reflections are not of the same kind, which justifies the additional term . For any point of a bright interference fringe, the course difference verifies:

For a given blade, the wavelength and the index are constant; the points corresponding to the same state of interferences, consequently at the same order of interferences verify:

Thus, interferences fringes are lines parallel to the intersection line of both diopters. These fringes are called “same thickness fringes”. The interfringe is obtained for a variation of order of one unity hence:

Considering that because angle is weak, we obtain:

The interfringe decreases when angle increases.

Both configurations that have just been studied, parallel sides blades and prismatic blades, are particularly important because we can find their concepts in Michelson interferometer and all interferometers derived from it.