Optics: Interference - Calculate Order of Maximum Intensity

[RESolo]

“Light is emitted with a central wavelength of 500 nm. First it is analysed with a Michelson Interferometer: starting from uniform illumination, one of the mirrors is displaced 2.5 mm until no new fringes can be distinguished. Then it is analysed with a Young´s Double Slit: it is observed that the intensity of the minima adjacent to a certain maximum is not zero, but 0.05% of the maximum intensity. What is the order of said maximum?”

So I don´t really have any idea what to do. I tried to obtain order m by finding the intensity ratio:
I_max/I_min =cos^2⁡(δ_max/2)/cos^2⁡(δ_min/2) =0.0005
Where:
δ_max/2=πm and δ_min/2=π(m+1/2)
But it turns out that m is not an integer, but 0.0071. And when I use the standard order equation for the interferometer, I get:
2∆d/λ=∆m
And this gives a change in m of about 10000!

Basically I don´t understand the link between the two parts of the question and any help would be appreciated.

 

[Asim Riaz]

You need to use both parts of the question in order to answer it. First, you need to use the Michelson Interferometer to calculate the change in order (Δm) due to the displacement of one of the mirrors (2.5 mm). The equation 2∆d/λ=∆m can be used to calculate the order change, where λ is the light's central wavelength (500 nm), and ∆d is the displacement of the mirror (2.5 mm). This will give you the order change due to the displacement of the mirror.Then, you can use the Young's Double Slit to calculate the order of the maximum intensity. You know that the ratio of the maximum intensity to the adjacent minimum intensity is 0.0005. This means that the ratio of the cosines is also 0.0005. Using this equation, you can solve for m, which is the order of the maximum intensity. Hope this helps!