Deriving formulas for laser wavelength measurement with Michelson interferometer

[kizersi5]

:!) My problem is that I am required to derive such formulae, which are:


MEASUREMENT of the LASER wavelength.


(1) 1 or lamda = 2* dm/m & (2) m=(n-1) ( 2*d/1)*(Dp/ Patm)

dm= distance of the movable mirror moved toward a beam splitter.

m= no. of fringes that cross a given reference point.

Dp = Pressure(final)- Pressure(initial)

d= distance of the vacuum air cell that was used upon experiment to generate fringes

Patm= atmospheric pressure=760atm.

I would appreciate any help deriving these formulae in step by step way.

 

[andrevdh]

A monochromatic beam (1) entering from the left splits up at B, a half silvered mirror, into two beams (2) and (3) and is reflected back by two mirrors. Beam (2) continues onwards to O and on its return (3) is reflected downward also to O (part of both beams actually since the mirror is half silvered). At O the beams are combined optically resulting interference of the two beams. If the paths of the two beams , (2) and (3), are the same length constructive interference will result at and a bright fringe will be observed at O. If the movable mirror is moved $\frac{\lambda}{4}$ closer to the beam splitter this condition will change to destructive interference. If the mirror is moved by $\frac{\lambda}{2}$ one fringe change will be observed at O. This gives you your first equation.