A Michelson interferometer operating at a 600 nm wavelength has a 3.59-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?

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ConcepcionPetillo ConcepcionPetillo · Answer 1 · 2019-12-11T04:45:55+01:00

Answer:

The number of bright dark fringe shifts is 35

Solution:

As per the question:

Wavelength of the light, [tex]\lambda = 600\ nm[/tex]

Refractive index of air, [tex]\mu_{a} = 1.0028[/tex]

Length, d = 3.59 cm

Now,

The no. of bright-dark fringe shifts can be calculated by the given formula:

[tex]m = (\mu - 1)\frac{2d}{\lambda}[/tex]

Thus

[tex]m = (\mu_{a} - 1)\frac{2d}{\lambda}[/tex]

[tex]m = (1.00028 - 1)\frac{2\times 3.59\times 10^{- 2}}{600\times 10^{- 9}}[/tex]

m = 33.5 ≈ 34