# Why do the Fringes in Michelson Interferometer move inward/outward?

We did this experiment using Michelson Interferometer of monochromatic source $$\lambda$$ to find the refractive index $$n$$ of dry air in a chamber of length $$L$$ by counting the number of fringes moved radially outwards as the pressure in the chamber decreases.

I am struggling to explain why do the fringes move outward when the pressure in the chamber decreases (We started from 290 torr and stopped at 120 torr).

This is my argument: As the pressure decreases, the refractive index is supposed to decrease (as $$n \propto p$$ for air $$\approx$$ ideal gas). This should reduce the path difference $$2(n-1)L$$ between the two interfering beams. The path difference between the incident and reflected beams is $$2d\cos\theta$$. $$\theta$$ is the angular separation of our fringe from the center. $$2d$$ is the mirror displacement but for our concern $$2d = 2(n-1)L$$ and thus we have the relation between $$n$$ and $$\theta$$ as $$P.D. = 2L(n-1)\cos\theta$$

For a bright fringe, $$m\lambda = 2L(n-1)\cos\theta$$. So for a given fringe, m is fixed and hence P.D is fixed. As $$n$$ decreases, $$\cos\theta$$ should increase in a way to keep P.D. constant.

But according to my argument, $$\theta$$ should decrease. That means I am wrong somewhere. But where?

• Can you describe the device in more detail ? How did you place the chamber in the interferometer? In front of one of the mirrors, like a glass slide? Commented Aug 18, 2021 at 14:33