Determining hole size using laser interference

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Homework Help Overview

The problem involves determining the diameter of a hole in aluminum foil using laser interference patterns observed on a wall. The setup includes a laser with a wavelength of 633 nm and a distance of 1.25 meters from the hole to the wall, with a noted spacing of 8 mm between interference maxima.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the application of a specific formula for calculating the hole diameter based on the observed interference pattern. Questions arise regarding the appropriateness of the formula used for a single hole versus a double-slit setup, as well as the accuracy of the value for the variable "k" in the equation.

Discussion Status

The discussion is ongoing, with participants providing insights into potential issues with the original poster's approach. There are suggestions to reconsider the formula used and to clarify the parameters involved in the problem setup. No consensus has been reached yet.

Contextual Notes

Participants note the possibility of a misunderstanding regarding the type of interference pattern being analyzed, specifically whether it pertains to Airy disks and their associated equations. There is also mention of a potential error in the reported distance between interference maxima.

Drizzy
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Homework Statement



upload_2016-12-11_22-31-15.png


Lisa makes a hole in aluminum foil. She wants to know the diameter of the hole. She points a laser through the hole. That picture is what appears on the wall that is 1,25 meters behind the aluminum. the distance between every circle is 8mm. the wave length is 633nm.

http://imgur.com/a/kcaPz

Homework Equations



dsinx=kλ

The Attempt at a Solution


[/B]
8mm between maximum 1 and 2. so I know that Tanx= 0.0008/1.25
x= arcTan(0.008/1.25)
d=kλ/sinx
d= 1*633*10-9/(sin(arcTan(0.008/1.25))

I get the wrong answer, why?
 
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What do you get for the sin(arcTan(0.008/1.25) ?
 
0.0063998689
 
Ok, so degrees and radians isn't the problem and I have to read the problem statement. Is your formula applicable for a single hole (as opposed to two slits) ?
 
yes
 
Check your value of "k".

Also, is there a slipped decimal in:
Drizzy said:
distance between every circle
 
Two things.

First, perhaps for learning purposes your class is using that simple equation, but that is not the correct equation for the ring spacing of an Airy disk. Are you sure your class didn't discuss Airy rings and present a slightly different formula?

Second, the distance to the first Airy minimum is different than the spacing of subsequent minima. You have to go above the first order to answer correctly.
 

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