I'm working with a Jamin interferometer, and I'm interested in calculating the intensity pattern I would observe in a far away plane. The scheme is as follows:
Spherical light enters through the interferometer's left dielectric. Part of it is reflected, part of it is transmitted. The reflected part (top beam) will cover a distance $L_1$ in the vacuum before entering the first tube (of length $L_2$), which is also in vacuum. It wil then exit the tube, cover a distance $L_3$ until it reaches the second dielectric, and then enter it, traveling a distance $L_4$, before being reflected an going down a distance $L_5$ still inside the dielectric, to finally exit it and cover a distance $L_6$ until it reaches the observation plane. The second beam will do the same (in reverse), the only difference being the second tube is not in vacuum but is filled with some dielectric material of refractive index $n$.
Since the initial beam is taken to be spherical and both end beams go to the same plate, and assuming the second dielectric is narrow enough so the end beams get superimposed, can is it valid to assume we can change the problem for an equivalent one where we have 2 virtual point-like sources one on top of another, just as is the case with the Michaelson interferometer? In that case, the distance of the first virtual source would be:
$$D_1=L_1+1\cdot L_2+L_3+n_dL_4+n_dL_5+L_6$$
where $n_d$ is the dielectric plate's refractive index. For the second beam, we would have:
$$D_2=n_dL_5+n_dL_4+L_3+nL_2+L_1+L_6$$
Now, recovering the result from the Micahaelson interferometer, if we placed the observation plane far away (at infinity), we would get an interference pattern such that:
$$I=4I_0cos^2\left(\frac{k}{2}(D_2-D_1)cos(\theta)\right)$$
Now, since we are in the same case as in the Michaelson (two point-like virtual sources which are on the line perpendicular to the observation plane, which is at the same time in infinity), then we can simply take this result and substitute our own $D_2-D_1$, for which we finally get:
$$\boxed{I_{Jamin}=4I_0cos^2\left(\frac{k}{2}(n-1)L_2cos(\theta)\right)}$$
Does this result make sense? Is my reasoning correct? I'm struggling to find information on Jamin's interferometer, and I can't contrast my work.
