Air Wedge radius of the wire Problem

In summary, an air wedge formed between two glass plates separated by a wire is illuminated with 600 nm light, resulting in 30 dark fringes. By understanding that the fringes correspond to integral numbers of wavelengths and that each fringe represents a change in thickness of half a wavelength, the radius of the wire can be calculated to be 4500 nm.
  • #1
Zukie91
15
0
Homework Statement
An air wedge is formed between two glass plates separated at one edge by a very fine wire. When the wedge is illuminated from above by 600 nm light, 30 dark fringes are observed. Calculate the radius of the wire.

The attempt at a solution
Wasn't really sure how to go about doing this, also don't have the answer, so i have no way of knowing if i am correct.
I think it has something to do with every time it goes light dark light, is one wavelength. not sure if that is relevant (or even correct) any help is appreciated.
Thanks
 
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  • #2
For this particular problem, the fringes correspond to integral numbers of wavelengths. As you go along to the next fringe it represents the next integral number wavelength phase difference which corresponds to a change in thickness of the air gap of half a wavelength. Thus there is a relationship between the maximum thickness of the air gap (i.e. the wire) the wavelength and the number of fringes. Can you work out what that must be?
 
  • #3
well, if there are 30 fringes, and each integral number wavelength phase dfference corresponds to a thickness of half a wavelength, would that mean at its thickest, the width is 15 wavelengths or 9000 nm?
 
  • #4
Yes that would be correct. But remember that the question asks for the radius of the wire.
 
  • #5
right, what i have there is the diameter, so i would divide by two and the final answer would be 450 nm. Thanks
 
  • #6
Zukie91 said:
right, what i have there is the diameter, so i would divide by two and the final answer would be 450 nm. Thanks

Careful! You're on the correct track though. :approve:
 
  • #7
whoops, typo, meant 4500 nm
 
  • #8
Zukie91 said:
whoops, typo, meant 4500 nm

very good.
 

FAQ: Air Wedge radius of the wire Problem

1. What is the Air Wedge radius of the wire problem?

The Air Wedge radius of the wire problem is a physics problem that involves calculating the radius of a wire using an air wedge setup. The air wedge is created by placing a piece of glass or plastic on top of a flat surface and then inserting a wire into the wedge. The goal is to determine the radius of the wire by measuring the distance between the wire and the surface at different points along the wedge.

2. How is the radius of the wire calculated in the Air Wedge problem?

The radius of the wire can be calculated by using the formula: r = (h^2 + t^2)/2h, where r is the radius, h is the height of the wedge, and t is the distance between the wire and the surface at a particular point on the wedge. This formula is derived from the geometric relationship between the radius, height, and distance of the wire in the air wedge setup.

3. What are the key factors that affect the accuracy of the Air Wedge radius calculation?

The accuracy of the Air Wedge radius calculation can be affected by a few key factors, including the precision of the measuring tools, the flatness of the surface, and the uniformity of the wedge. Any errors in these factors can lead to inaccuracies in the final calculation of the wire's radius.

4. How can the Air Wedge radius problem be applied in real-life situations?

The Air Wedge radius problem has practical applications in various fields, such as engineering, manufacturing, and research. It can be used to measure the diameter of wires or tubes in industrial settings, or to determine the thickness of thin films in materials science. It can also be used to calibrate measuring instruments and to test the accuracy of optical devices.

5. Are there any limitations to the Air Wedge radius problem?

While the Air Wedge radius problem is a useful tool for measuring small dimensions, it does have some limitations. For instance, it is not suitable for measuring very large or thick objects. Additionally, the accuracy of the calculation can be affected by external factors such as temperature and pressure changes, which can alter the dimensions of the air wedge setup.

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