Finding the Optimal Lens for Focusing a Helium-Neon Laser Beam

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In summary, a scientist is trying to focus a helium-neon laser beam with a wavelength of 633nm to a 10 micrometre diameter spot 8.0 cm behind the lens. They need to determine the focal length and minimum diameter to achieve this. Using the equations w = (2.44lambda * focal length) / diameter and theta = 1.22lamda/diameter, the minimum diameter is approximately equal to 2.5lambda. However, if a separate method is used, this can be ignored. The attempted solution involved calculating w through 2.5lambda and then using that to calculate the focal length, resulting in an answer of 0.001cm. However, this felt too small and
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strikingleafs01
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1. Homework Statement

A scientist needs to focus a helium-neon laser beam (lamda = 633nm) to a 10 micrometre diameter spot 8.0 cm behind the lens.

a) What focal-length should she use?
b) What minimum diameter should she use?

2. Homework Equations

w = (2.44lambda * focal length) / diameter

theta = 1.22lamda/diameter

Wmin is apprx equal to 2.5lambda...apparently, but if you have a separate method ignore this.

3. The Attempt at a Solution

i attempted to calculate w through 2.5lambda, then use that to calculate the focal length. the answer i got was 0.001cm.
 
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this felt a bit too small and made me think i was missing something..so then i tried to use w=2.44lambda*focal length/diameter, but i'm not sure how to go about solving the equation for focal length!any help would be greatly appreciated!
 

1. What is a helium-laser beam?

A helium-laser beam is a type of laser that uses helium gas as the active medium to generate a highly focused and powerful beam of light. It is commonly used in scientific research and industrial applications.

2. How does a helium-laser beam work?

A helium-laser beam works by exciting helium atoms with electricity, causing them to emit photons of light. These photons are then amplified by bouncing back and forth between two mirrors, creating a coherent and focused beam of light.

3. What are the advantages of using a helium-laser beam?

Some advantages of using a helium-laser beam include its high power and precision, as well as its ability to produce a narrow wavelength of light. It is also relatively compact and easy to control.

4. What are some common applications of helium-laser beams?

Helium-laser beams have a wide range of applications, including laser cutting and welding, spectroscopy, holography, and medical procedures such as eye surgery. They are also used in scientific research for precision measurements and experiments.

5. Are there any potential dangers associated with helium-laser beams?

Yes, there are potential dangers associated with helium-laser beams. They can cause eye and skin damage if not used properly, and the high power of the beam can also pose a fire hazard. It is important to follow safety protocols and wear appropriate protective equipment when working with helium-laser beams.

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