To develop this problem it is necessary to apply the optical concepts related to the phase difference between two or more materials.
By definition we know that the phase between two light waves that are traveling on different materials (in this case also two) is given by the equation
[tex]\Phi = 2\pi(\frac{L}{\lambda}(n_1-n_2))[/tex]
Where
L = Thickness
n = Index of refraction of each material
[tex]\lambda =[/tex] Wavelength
Our values are given as
[tex]\Phi = 7(2\pi)[/tex]
[tex]L=t[/tex]
[tex]n_1 = 1.58[/tex]
[tex]n_2 = 1[/tex]
[tex]\lambda = 550nm[/tex]
Replacing our values at the previous equation we have
[tex]\Phi = 2\pi(\frac{L}{\lambda}(n_1-n_2))[/tex]
[tex]7(2\pi) = 2\pi(\frac{t}{\lambda}(1.58-1))[/tex]
[tex]t = \frac{7*550}{1.58-1}[/tex]
[tex]t = 6637.931nm \approx 6.64\mu m[/tex]
Therefore the thickness of the mica is 6.64μm
