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A Michelson interferometer operating at a 400 nm wavelength has a 3.70-cm-long glass cell in one arm. To begin, the air is pumped out of the cell and mirror M2 is adjusted to produce a bright spot at the center of the interference pattern. Then a valve is opened and air is slowly admitted into the cell. The index of refraction of air at 1.00 atm pressure is 1.00028.
How many bright-dark-bright fringe shifts are observed as the cell fills with air?

Sagot :

Okpalawalter8idn

Answer:

[tex]m=42\ fringes[/tex]

Explanation:

From the question we are told that:

Wavelength [tex]\lambda=400nm[/tex]

Length of cell arm [tex]h=3.70cm[/tex]

Refraction of air at  at 1.00 atm pressure [tex]n=1.00028.[/tex]

Generally the equation for Number of shifts is mathematically given by

[tex]m=N-N_o[/tex]

Since

[tex]N_0=\frac{2t}{\lambda_0}[/tex]

Therefore

[tex]m=\frac{2t}{\lambda_0/n}-\frac{2t}{\lambda_0}[/tex]

[tex]m=\frac{2t}{\lambda_0} n-1[/tex]

[tex]m=\frac{2(3.7*10^{-2})}{400*10^{-9}}*(1.00028-1)[/tex]

[tex]m=51.8[/tex]

[tex]m=42\ fringes[/tex]

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