Math problem in Huygens-Fresnel principle

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In summary, the conversation discusses the Huygens-Fresnel principle, which involves a spherical wave point source and secondary sources on a spherical surface. The formula U(P)=K*∫∫U(Q)*F(θ0，θ0)*exp{ikr}/r*d∑ is used to calculate the light coming from these secondary sources at point P. The inclination factor, d∑, and integration process are all explained in Beam Optics books. The speaker is confused about the formula and requests a clearer explanation.
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mensa
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in Huygens-Fresnel principle, U(P)=K*∫∫U(Q)*F(θ0，θ0)*exp{ikr}/r*d∑
K=-i/λ; F(θ0，θ0)=0.5(cosθ0+cosθ) is inclination factor; d∑ is a small part of any close surfaces; these are all include in any Beam Optics book

I want to demonstrate the spherical wave point source S gives out, all the d∑ in the spherical surface as Secondary Source, whose light come to point P, equals to S only

I don't know how to integrate,coz it seems to hard to me.
Please show the process. Any book involves is available too.Thanks
 

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I'm so confused that no one could give me any answer...Is it because I didn't get the idea through? Please let me know...thx
 
  • #3
I can't understand the formula U(P)=K*∫∫U(Q)*F(θ0，θ0)*exp{ikr}/r*d∑.
Can you express it more clearly?
 

1. What is the Huygens-Fresnel principle?

The Huygens-Fresnel principle, also known as the Huygens principle, is a fundamental concept in optics that explains how waves propagate through a medium. It states that every point on a wavefront acts as a source of secondary spherical waves, and the sum of these waves determines the shape of the wavefront at a later time. This principle is used to explain diffraction and interference phenomena in optics.

2. How is the Huygens-Fresnel principle applied in math problems?

In math problems, the Huygens-Fresnel principle is used to calculate the diffraction pattern of a wave passing through an aperture or obstacle. This involves breaking down the wave into multiple secondary wavelets, and then using the principle to determine the amplitude and phase of each wavelet. By summing these wavelets, the overall diffraction pattern can be determined.

3. What is the significance of the Huygens-Fresnel principle in optics?

The Huygens-Fresnel principle is significant in optics because it provides a qualitative explanation for the behavior of waves, particularly in diffraction and interference. It also serves as the basis for more advanced mathematical models and calculations in optics, such as the Kirchhoff diffraction formula.

4. Can the Huygens-Fresnel principle be applied to all types of waves?

Yes, the Huygens-Fresnel principle can be applied to all types of waves, including electromagnetic waves, sound waves, and water waves. It is a fundamental principle that applies to any type of propagating wave.

5. What are some practical applications of the Huygens-Fresnel principle?

The Huygens-Fresnel principle has many practical applications in optics, including the design of lenses, telescopes, and other optical instruments. It is also used in the analysis and design of diffraction gratings, which are used in many technologies including CD and DVD players. In addition, the principle is applied in fields such as radar, sonar, and medical imaging to understand how waves behave and interact with obstacles and apertures.

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