Discover How to Measure Laser Wavelength with Modern Physics - HELP 911

[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.

 

[quicknote]

I can provide you with the steps to derive the formulae you mentioned. First, let's start with the formula for the wavelength of the laser, which is given by:

λ = 2dM/m

Where:
λ is the wavelength of the laser
dM is the distance the movable mirror is moved
m is the number of fringes that cross a given reference point

To understand this formula, we need to understand the concept of interference. When a laser beam is passed through a beam splitter, it gets divided into two beams. These two beams then interfere with each other, resulting in a pattern of bright and dark fringes. The distance between these fringes is directly related to the wavelength of the laser.

Now, let's look at the formula for m, which is given by:

m = (n-1)(2d/λ)(Δp/Patm)

Where:
m is the number of fringes
n is the refractive index of the medium
d is the distance of the vacuum air cell
λ is the wavelength of the laser
Δp is the change in pressure
Patm is the atmospheric pressure

To derive this formula, we need to understand the concept of pressure and refractive index. When a laser beam passes through a medium (such as air), its wavelength changes due to the change in refractive index. This change in refractive index is directly related to the change in pressure.

By combining these two concepts, we get the formula for m. To derive this formula, we need to use Snell's law and the formula for the refractive index of a medium.

I hope this helps you understand the derivation of these formulae. Keep in mind that these formulae are based on certain assumptions and may not be applicable in all cases. It is always important to consider the experimental setup and conditions when using these formulae for measuring the wavelength of a laser.