What is Fresnel: Definition and 124 Discussions

Augustin-Jean Fresnel ( FRAYN-, FREN-el, -⁠əl or fray-NEL; French: [oɡystɛ̃ ʒɑ̃ fʁɛnɛl]; 10 May 1788 – 14 July 1827) was a French civil engineer and physicist whose research in optics led to the almost unanimous acceptance of the wave theory of light, excluding any remnant of Newton's corpuscular theory, from the late 1830s  until the end of the 19th century. He is perhaps better known for inventing the catadioptric (reflective/refractive) Fresnel lens and for pioneering the use of "stepped" lenses to extend the visibility of lighthouses, saving countless lives at sea. The simpler dioptric (purely refractive) stepped lens, first proposed by Count Buffon  and independently reinvented by Fresnel, is used in screen magnifiers and in condenser lenses for overhead projectors.
By expressing Huygens's principle of secondary waves and Young's principle of interference in quantitative terms, and supposing that simple colors consist of sinusoidal waves, Fresnel gave the first satisfactory explanation of diffraction by straight edges, including the first satisfactory wave-based explanation of rectilinear propagation. Part of his argument was a proof that the addition of sinusoidal functions of the same frequency but different phases is analogous to the addition of forces with different directions. By further supposing that light waves are purely transverse, Fresnel explained the nature of polarization, the mechanism of chromatic polarization, and the transmission and reflection coefficients at the interface between two transparent isotropic media. Then, by generalizing the direction-speed-polarization relation for calcite, he accounted for the directions and polarizations of the refracted rays in doubly-refractive crystals of the biaxial class (those for which Huygens's secondary wavefronts are not axisymmetric). The period between the first publication of his pure-transverse-wave hypothesis, and the submission of his first correct solution to the biaxial problem, was less than a year.
Later, he coined the terms linear polarization, circular polarization, and elliptical polarization, explained how optical rotation could be understood as a difference in propagation speeds for the two directions of circular polarization, and (by allowing the reflection coefficient to be complex) accounted for the change in polarization due to total internal reflection, as exploited in the Fresnel rhomb. Defenders of the established corpuscular theory could not match his quantitative explanations of so many phenomena on so few assumptions.
Fresnel had a lifelong battle with tuberculosis, to which he succumbed at the age of 39. Although he did not become a public celebrity in his lifetime, he lived just long enough to receive due recognition from his peers, including (on his deathbed) the Rumford Medal of the Royal Society of London, and his name is ubiquitous in the modern terminology of optics and waves. After the wave theory of light was subsumed by Maxwell's electromagnetic theory in the 1860s, some attention was diverted from the magnitude of Fresnel's contribution. In the period between Fresnel's unification of physical optics and Maxwell's wider unification, a contemporary authority, Humphrey Lloyd, described Fresnel's transverse-wave theory as "the noblest fabric which has ever adorned the domain of physical science, Newton's system of the universe alone excepted." 

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  1. K

    B Calculating non-dielectric reflectance without using complex numbers

    I need a to calculate the fresnel reflection ratio of a non dielectric material given the incident angle, the refractive indexes of the incident and interfacing materials and the extinction coefficient of the interfacing material. I need to to this without directly using complex numbers, due to...
  2. yucheng

    I Validity of Fresnel Approximation

    Wikipedia says that Fresnel diffraction is valid if the Fresnel number is approximately 1. What Fresnel number then is the Fresnel approximation for paraxial-paraboloidal waves valid? It's not mentioned... Oh I just realized that $$\frac{N_F \theta_m^2}{4} \ll 1$$ So it depends on the maximum...
  3. Bernadette

    B A variation on the Fresnel Spot experiment

    Hello Fresnel discovered that the shadow of a small disc had a bright point in its center. Experiment that he carried out by letting sunlight pass through a small hole (quasi-point source). If, instead of looking at the shadow of the disk, we look (*) in the direction of the light source...
  4. B

    Show that the solutions to the Fresnel Equation are real and positive

    I got as far as simplifying the expression to $$\frac{4}{9}(n_x^4 n_y^4 + n_x^4 n_z^4 + n_y^4 + n_z^4 - n_x^4 n_y^2 n_z^2 - n_x^2 n_y^4 n_z^2 - n_x^2 n_y^2 n_z^4)$$ But that doesn't seem to be a form that is necessarily positive and satisfies the criteria of the homework statement. Little help...
  5. Douglas-Stinson

    A Calculating Fresnel Diffraction Pattern from Circular Apertures

    I am attempting to calculate the Fresnel difraction pattern from different diameter circular apertures for specific source to aperture and aperture to sensor distances. I'm generally following the procedure given in Klaus D. Mielenz "Algorithms for Fresnel Diffraction at Rectabngual and Circular...
  6. ergospherical

    Fresnel diffraction from square: on axis intensity

    I'd appreciate if someone could check whether my work is correct. The ##x##-##y## symmetry of the aperture separates the Fresnel integral:\begin{align*} a_p \propto \int_{-a/2}^{a/2} \mathrm{exp}\left(\frac{ikx^2}{2R} \right) dx \int_{-a/2}^{a/2} \mathrm{exp}\left(\frac{iky^2}{2R} \right) dy...
  7. J

    I Fresnel equations and conservation of energy (phase shifts)

    Quantum mechanically speaking when we split a wave in two the resulting waves must have a 90 degrees phase difference for energy to be conserved. Take the beamsplitter depicted in [1] for example. But the Fresnel equations state that the reflected wave should experience a phase shift of π when...
  8. J

    I Using Diffraction (i.e., Fresnel Zone Plate) to defocus/diverge light

    I am wondering if it is possible to use principals of diffraction to cause a collimated beam of light (laser) to become divergent. I see that zone plates are most always used for focusing the light from a source, unless they are used in reverse. This is why zone plates are seemingly always...
  9. Mr_Allod

    Reflection and Refraction in an Elliptical Imaging Mirror

    My thoughts so far: a. Since the critical angle occurs at the origin for the given parameters I would imagine that the maximum power reflected would be 100% since at the critical angle ##\theta_t = \frac \pi 2## and ##r_ {\perp} = r_{\parallel} = 1##. I do not know how I might go about finding...
  10. Athenian

    Fresnel Equations for the Power of Reflectance and Transmittance

    I understand that the power of reflectance and the power of transmittance (regardless of it being S-polarized or P-polarized light), when added together, would equal to one. In other words, ##R+T=1##. However, how do I go about checking for this fact? Using the equations from the "Relevant...
  11. T

    What are the key considerations for imaging with a condenser fresnel lens?

    Hello All, I am in need of an optics expert on imaging, and in particular a fresnel lens is being used as for an imaging device. From my understanding a condenser lens can be considered equivalent to a plano-convex lens. Setup: A condenser fresnel lens is used, for which both the fresnel and...
  12. Sokolov

    Irradiance of light trapped between two parallel mirrors

    The setup of the problem is shown in the image below. I know that I must add all the contributions of each reflected ray and that its amplitude will be reduced by a factor ##r## each time it is reflected. So after the n-th reflection, its amplitude will be ##E_0r^n##, with ##E_0## the amplitude...
  13. K

    Real Fresnel diffraction experiment

    I'm wondering if I can perform an actual experiment to observe Fresnel diffraction. I would like to do it with a rectangular aperture and of course, visible light. What should its dimensions be? And from which distance from it can I expect to start seeing a decent diffraction pattern? I know I...
  14. XLAYZ

    Do the Fresnel equations of reflection apply to monochromatic light?

    Hello, I have a monochromatic light source (wavelength ~ 420 nm), which will be incident on the interface of two different media. Could someone please explain if the Fresnel equations applies with monochromatic light when estimating the reflectance and transmitance? Thank you in advance...
  15. Lucas Olivio

    Understanding the Mathematical Explanation for Fresnel Lenses

    Homework Statement: what is the mathematical explanation for fresnel lenses Homework Equations: No equations were provided I'm going to post a link to one article I found that I think has the answer, but I couldn't understand because of my lack of knowledge in physics and math...
  16. MarcelComsol

    Fresnel Equations Simulation in 2D: How to Avoid Side Entry in Comsol?

    Hi there, I'm failing in simulating the fresnel equations in 2D with Comsol. As you can see in the model added to this post, the reflectance and transmission in the global plots both for TE-waves ("Port, senkrecht polarisiert", Plot "Reflektion und Transimission, senkrecht") and TM-waves...
  17. Cathr

    Finding Fresnel coefficients from the interface conditions

    Homework Statement We have an incident electric field, and there are two cases: 1) the field is polasised perpendicularly to the incidence plane (TE) 2) polarised in the plane (TM) Here I must be able to correctly apply the limit conditions, to find the Fresnel formulas that give the...
  18. Cathr

    I Finding the Fresnel coefficients from interface conditions

    I'm studying for an exam (so this is existential) and I never really got how to write the limit conditions for an interface. In my problem, there is an incident electric field, and there are two cases: 1) the field is polasised perpendicularly to the incidence plane (TE) 2) polarised in the...
  19. F

    A Fresnel Diffraction - Opaque Barrier Question

    Hello! I'm very interested in knowing your opinion on how close my model is to the Fresnel Diffraction by an opaque barrier, as seen here: http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/difopa.html#c1 My model: Sorry for the low quality image.
  20. S

    Fresnel Equations and Snell's Law

    Homework Statement From the Fresnel equations and Snell’s Law, prove that, when θ = θB where tanθB = nt/ni, (θB is the Brewster angle); (a) Reflection coefficient = 0 , and (b) transmission coefficient = n/n’ Homework Equations reflection coefficient = (ntcosθi - nicosθt) / (ntcosθi + nicosθt)...
  21. S

    Fresnel equation and Snell's law

    Homework Statement Use Snell's law to show fresnel Eq 1 can be expressed as Eq 2 Eq 1 = (ncosθ-n'cosθ') / (ncosθ+n'cosθ) Eq 2 = (tanθ' - tanθ) / (tanθ' + tanθ) Homework Equations nsinθ=n'sinθ' (Snell's law) The Attempt at a Solution n' = nsinθ / sinθ' Substitute n' into equation and then...
  22. C

    MATLAB FFT problem for Fresnel simulation

    Hi all, I'm trying to simulate the Fresnel diffraction by using this expersion : $$ A(x')=\frac{1}{j\lambda z}e^{jk(z+\frac{x'^2}{2z})}F(A^{trans}(x)e^{jk\frac{x^2}{2z}})_{u=\frac{x'}{\lambda z}} $$ So when I use this formula my problem is that I don't know how to take the good frequency, here...
  23. T

    What's the amount of energy lost in Total Internal Reflection?

    In Total Internal Reflection, the beam can still lose some energy as it reflects off the boundary of the medium it is within. This isn't covered under the Fresnel equations. The energy loss is probably lost in the form of evanescent waves. I tried searching for the formulae describing the...
  24. H

    Finding Uniform Focusing in Flexible Fresnel Lenses

    Well this thread title sucks, sorry. << Mentor Note: Title Edited>> :smile: I have a plano convex lens (actually equivalent stack of two fresnels each with focal length 120mm, groove pitch: 0.3mm). If I put a photo behind it at a 45mm distance and view through the lens from a 12mm distane, I...
  25. S

    Optical Can a DIY Fresnel Lens Concentrator be Created Using a Rotating Liquid Mold?

    Just running an idea for a diy fresnel lens past .. [ In the context that parabolic mirrors have been created by rotating a liquid ] The volume left above the parabola is also parabolic, so ...if that volume is used as a mold for casting it should form a reasonable solid lens, at least for...
  26. D

    MHB Evaluate Case of Fresnel Integral

    Evaluate $\lim\limits_{{n}\to{\infty}} \int_{n}^{n+1} \cos^2(x^2) \,dx$ I've tried using the half angle identity and the taylor series on the remaining $1/2 + \cos(2x^2)$ to prove the value is $1/2$, but I am out of ideas.
  27. G

    Are the Fresnel coefficients equal for E and B fields?

    From the Maxwell Equations we know that there are four boundary conditions for an electromagnetic wave crossing an interface between two dielectric media. For the TE polarisation state, these conditions give us that E_{i} + E_{r} = E_{t} B_{i}\,\cos\theta_{i} - B_{r}\,\cos\theta_{r} =...
  28. D

    Multiple reflections and transmissions of light inside a cube

    Imagine I have a 10x10x10cm cube filled with a scintillating material (material capable of generating light when energized). Three cameras are looking at this cube from three orthogonal directions (x, y, and z). Light is generated inside the cube and is refracted as it leaves the cube and...
  29. G

    I Overview of General Fresnel Equations + Complex IORs

    Hi, My understanding is that when light (with some frequency and polarization) hits the interface between two media (each with some frequency-dependent material properties), the Fresnel equations apply. This tells us how much light reflects back versus refracts across the interface. I'm...
  30. binbagsss

    Inequality quick question context cauchy fresnel integral

    Homework Statement please see attached, I am stuck on the second inequality. Homework Equations attached The Attempt at a Solution I have no idea where the ##2/\pi## has come from, I'm guessing it is a bound on ##sin \theta ## for ##\theta## between ##\pi/4## and ##0## ? I know ##sin...
  31. Latempe

    For the Fresnel Equations for TM light why is 1 + r not t?

    The complex amplitude ratios for light are defined as: rTM = ErTM / EiTM tTM = EtTM / EtTM I've done the derivation from Wikipedia and see that (n2/n1) * tTM = rTM + 1. But I don't understand what is going on physically. I understand that these values are not power or intensity so I can't...
  32. JulienB

    Fresnel zones of a planar wavefront

    Homework Statement Hi everybody! I'd like to ask you guys some details about the following problem: Determine the area of the l-th Fresnel zone of a planar wavefront considered from a point P. Give the numerical result for the 1st Fresnel zone for a wavelength ##\lambda=600##nm and a distance...
  33. J

    MHB Integral of Fresnel functions

    I have been working on this for several days but getting nowhere. Any help would be great. \begin{align} &\int_0^x dy\,y^2 \cos(y^2) C^2 \!\!\left(\!\frac{\sqrt{2}\,y}{\sqrt\pi}\!\right) \end{align} In reality only the first one is causing me troubles, however I have pasted the entire...
  34. Alvis

    Not a homwork problem, Fresnel Equations

    Homework Statement I was just curious, I know you can derive the critical angle using Snell's law..but could you use it using the Fresnel Equations of reflection, both of them? Homework Equations |r|=1 internal reflection of light...
  35. J

    Fresnel reflection coefficient for Second Harmonic Generation (SHG)

    Hello everyone, this is my first post so I don't know whether or not this is the right thread to be asking this question (if so I am sorry). I am currently working on my thesis where I am determining the thickness of a GaN crystal through second harmonic generation. However in a article...
  36. bananabandana

    I Confusion With Derivation of Fresnel Equations

    Okay, so I'm working with the diagrams above. ##i## denotes incident, ##r## reflected, and ##t## transmitted. -We're working in two HIL dielectrics. Incoming and outgoing waves are of form ##Aexp[i(\vec{k}\cdot\vec{r}- \omega t) ##. As I understand it, Maxwell's equations give four boundary...
  37. T

    A Understanding Reflectance with Fresnel Equation for Non-Polarized Light

    Hi All, I am new to this forum. We are researching light reflection from carbon nanotubes. Now I know about the Fresnel Equation that can be used to determine reflectance for S (perpendicular to the plane of the incident) and P (parallel to the plane of the incident) polarized light.Now, if I...
  38. S

    Fresnel Loss & Brewster's Angle

    Homework Statement I'm trying to understand these two a bit better in terms of lasers. Fresnel Loss - The loss that occurs when there is a change in refractive index. Some light will be transmitted, while other light will be reflected back into the medium. This is bad for lasers because it...
  39. tommowg

    Using Fresnel Formulae and Poynting vector problem

    Homework Statement I'm having a problem using the fresnel formulae for these two problems below: 1. Using Fresnel formulae and expression for the Poynting vector show that at the interface between two dielectrics in the absence of absorption R+T=1, where R – is reflectivity and T –...
  40. I

    Evaluating Fresnel Integrals Using Euler Formula

    Homework Statement Evaluate the following integrals C = 0inf∫cos(x2) dx and S = 0inf∫sin(x2) dx Homework Equations [/B] Hint: use Euler formula to write the integral for F = C + iS. Square the integral and evaluate it in polar coordinates. Temporary add a convergence factor. Answer: C = S =...
  41. D

    Fresnel zone and reflection of light on surfaces

    In a Scientific American article from 1968 in which he explains classically how light interacts with matter, Victor Weisskopf states that "the reflection of light on the surface of a solid or liquid involves only the oscillators (electrons) located in a small, pillbox-shaped volume at the...
  42. Vaibhav DixiT

    Fresnel Diffraction through a straight edge

    I read in texts that when a rays of light are diffracted from a straight edge, the phenomenon can be explained using the half period zones. The things that is confusing me is this: "Odd number of half period zones, if exposed, lead to a bright fringe. Even number of half period zones exposed...
  43. fluidistic

    Derivation of Fresnel equations / minus sign

    Homework Statement For an s-polarized wave (E and B fields are orthogonal to the plane of incidence) passing from medium to medium 2, I'm not understanding a minus sign. The matching conditions are ##\hat n \times (\vec E_2 - \vec E_1)=\vec 0## and ##\hat n \times (\vec H_2 - \vec H_1 )=\vec...
  44. Abtinnn

    Generalization of Fresnel Equations?

    Hi guys! I was wondering if there is a generalization to the Fresnel equations. Those equations calculate the reflective and transmissive coefficients, but it depends on the polarization of the incident ray. Is there a formula that could calculate those constants for an unpolarized incident...
  45. E

    Fresnel Relations and the Sensitivity of a Camera

    Reflectance, according to the Fresnel Relations, is given by ##R \equiv \frac{I_r}{I_i}##, and Transmittance is ##T = \frac{I_t \cos \theta_t}{I_i \cos \theta_i}##. Do these values depend on the wavelength of light? For example, if I have a beam of white light rather than a monochromatic...
  46. E

    MATLAB Implementation of Fresnel Diffraction in MatLab

    I'm trying to simulate the Fresnel Diffraction in MatLab using the Fast Fourier Transform syntax. But I'm not getting really good diffraction patterns. Here is the code: %% Fourier Transform for G(p, q) g = layer.*exp(((1i*pi)/(lambda*z))*(r_obj)); G = fftshift(fft2(g)); %% Fourier Transform...
  47. E

    Computer Simulation of Fresnel Diffraction

    Considering this system (from Wikipedia), The Fresnel Diffraction at x, y, and z is ##E \left(x, y, z\right) = \frac{z}{i \lambda} \int \int^{+\infty}_{-\infty} E \left(x', y', 0\right) \frac{e^{ikr}}{r^2} dx' dy'## where ##r = \sqrt{\left(x - x'\right)^2 + \left(y - y'\right)^2 + z^2}##...
  48. S

    Calculating Focal Length of 1D Fresnel Lens

    Homework Statement Calculate the focal length of 1D Fresnel lens, whose transmittance is given as $$T(\xi)=\frac 1 2(1+\cos(\alpha \xi ^2)).$$ Homework Equations Anything you wish The Attempt at a Solution I have no idea. I tried to use the equation for diffraction image $$u_p=C\int _0...
  49. I

    A problem about Fresnel fringes of electron microscopy

    My question is simple: Why do the Fresnel fringes at the edge of a hole in a reticulated carbon film become larger and more widely spaced when the defocus is increased? This occurs whether you are over focused or under focused, right? But why?
  50. S

    What is the index of refraction of the glass in this reflection problem?

    Homework Statement Unpolarized light hits a flat glass surface, 37.5 degrees to the surface's normal. The reflected light's polarization is investigated with a polaroid. The relationship between the max and min value of intensity from the polaroid when it is rotated is 4.0. What is the index of...