One leg of a michelson interferometer contains an evacuated cylinder of length l, having glass plates on each end. a gas is slowly leaked into the cylinder until a pressure of 1 atm is reached. if n bright fringes pass on the screen when light of wavelength λ is used, provide an expression for the index of refraction of the gas?
hint: the fringe shifts occur because the wavelength of the light changes inside the gas-filled tube.

Explanation:

Due to  change in the refractive index of the medium , wavelength changes. If λ  be wave length in vacuum ,  wave-length in refractive index μ

will become  λ / μ

Initially no of wavelengths in length L were  L / λ

Finally no of wavelengths in length L were L / λ / μ = Lμ / λ

Given

Lμ / λ  -  L / λ  = N

L / λ ( μ -1 ) = N

μ = ( Nλ / L + 1 )

  the grams     of oxygen gas   that can be produced     is 20.6   grams of o₂

calculation

2liclo₃ →   2 licl + 3 o₂

step 1:   find the moles of liclo₃

moles = mass÷ molar mass

from periodic table the molar mass of liclo₃ =6.9 +35.5   +(16 x3) =90.4 g/mol

moles=38.7 g÷90.4 g/mol=0.4281   moles

step 2:   use the   mole ratio   to calculate the moles of o2

from equation above, liclo₃: o₂   is 2: 3  

therefore the moles of   o₂=0.4281 moles x3/2 =0.6422   moles

step 3: find mass   of o₂

mass= moles x molar mass

from periodic table the   molar mass of   o₂ = 16 x2= 32 g/mol

mass=0.6422   moles   x   32 g/mol = 20.6 grams of o₂