Problem and thoughts about simple light interference

[Mr.P]

1. With the later on given info, is it possible to through geometry calculate the wave length of a HeNe Laser?


2. Homework Equations and facts

A Helium Neon laser emitts light through a double slit and towards a screen where a central image and the first dimmer bands can be seen.
The distance from the the HeNe laser to the screen is 757 cm, and the distance between the central band and the dimmer bands are 6 cm.
The frequency and the width of the double slit are both unknown factors.

3. The Attempt at a Solution

With the Pythagorean theorem the distance between the double slit and the screen can be calucaled, and with "simple geometry" the directional angle can be calculated.
I am thinking that the if one calculates the difference of

1. the distance between the double slit and the central band

and

2. the distance between the double slit and the nearest dimmer band

the answer could also be the wave length of the laser?
However, the answer of the calculation which is 757 minus the squareroot of (757^2+6^2) = 0,023777 cm. And since the HeNe lasers has a wave length somewhere around 630 nm I am suspecting my theory is off.

Most grateful for any shared thoughts on this,

Pete

 

[lanedance]

hey Mr.P

for any given path (ie angle) it is actually the difference in path length between the rays from each of the 2 slits, that causes the interference

not the overall path length difference between different angle as you have calculated

To calculate this you need to know th slit length. DO you know the double slit formula or can you draw a picture & clculate it?

without doing the math I'm not 100%, but its my guess that you can only determine the ratio of slit spacing to wavelength, not the absolute wavelength

 

[Mr.P]

Hej Lanedance,

thanks for taking the time. The slit length is never specified so the slit formula cannot be applied to get the wave length.

I made and attached a simple sketch of the problems setup, but I guess since the difference in overall path length between the two paths doesn't correspond to the wave length I am off in my theory.

I assume the wave lentgh in this problem cannot be determined with geometry, only with a value for the slit length. (?)

Once more thanks for your time,

Pete from Sweden