Determining hole size using laser interference

• Drizzy
In summary, Lisa makes a hole in aluminum foil and points a laser through it. The resulting image on a wall 1.25 meters behind the aluminum shows circles with a distance of 8mm between them. Using the formula dsinx=kλ, Lisa attempts to calculate the diameter of the hole but gets the wrong answer. After checking the formula and considering the distance between the circles, it is determined that the formula may not be applicable for a single hole and the value of "k" needs to be checked. Additionally, the formula used may not be the correct one for calculating the spacing of the rings, as the distance to the first Airy minimum is different than the spacing of subsequent minima.
Drizzy

Homework Statement

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

dsinx=kλ

The Attempt at a Solution

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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?

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.

1. How does laser interference help determine hole size?

Laser interference is a measurement technique that uses the interference pattern created by two laser beams to accurately determine the diameter of a hole. As the laser beams pass through the hole, they create a distinct interference pattern that can be measured and analyzed to determine the size of the hole.

2. What are the advantages of using laser interference for hole size determination?

One major advantage of using laser interference is its high precision and accuracy. The interference pattern is highly sensitive to even small changes in the diameter of the hole, making it a very precise measurement technique. Additionally, it is a non-contact method, meaning there is no physical contact with the hole or object being measured, reducing the risk of damage or distortion.

3. Are there any limitations to using laser interference for hole size determination?

While laser interference is a highly accurate method, it does have some limitations. It is most effective for measuring holes with diameters between 0.1-10 millimeters. Holes that are smaller or larger than this range may not produce a clear interference pattern and may require a different measurement technique.

4. What factors can affect the accuracy of laser interference measurements?

The accuracy of laser interference measurements can be affected by factors such as the quality and stability of the laser source, the alignment of the laser beams, and the surface roughness and material of the object being measured. It is important to carefully control these factors to ensure accurate results.

5. How can laser interference be used in real-world applications?

Laser interference is commonly used in industries such as manufacturing and quality control to measure the dimensions of small holes in various materials. It is also used in scientific research for analyzing microscopic structures and in medical imaging for non-invasive measurements of bodily tissues and organs.

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