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Thread: 1.74 index and Abbe value...

  1. #1
    sub specie aeternitatis Pete Hanlin's Avatar
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    Well, I see Seiko is introducing a 1.74 index lens (Vision Monday, vol. 14, iss. 14; pg.40). The article mentioned the lens has an abbe value of 33.

    This brings me to my latest question...

    What property(ties) of a material determine abbe value? For that matter, what properties dictate the index of refraction? In other words, WHY does poly carbonate disperse light to a greater degree than allyl diglycol carbonate?

    Thanks in advance for your answers. I always enjoy reading them because they introduce me to new areas of science (and I usually comprehend most of what you are saying). I'm just waiting for someone to ask a question about soteriology or transubstantiation so I can excersize my Theological synapses!

    Pete

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    Master OptiBoarder Jeff Trail's Avatar
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    [QUOTE]Originally posted by Pete Hanlin:
    [I]
    What property(ties) of a material determine abbe value? [QUOTE]

    Pete,

    I'll give it a try and then let everyone else "correct" me (Darris,Daryl etc. etc.) :)

    To figure out dispersion and abbe numbers you figure that light travels at about 186,000 MPS in a vacuum, when a ray or wave enters any material it slows down. Different waves will slow different amounts.
    The same goes for wavelengths in the visible spectrum as well. Red waves (660nm) will travel at a different speed in than blue (460nm) The index of refraction is measured in yellow light (588nm).. So actually the index of any given material can vary depending on the wavelength of the light ray :)
    In our little end of the industry (optics) shorter waves are slowed more then longer waves. Our concern is mostly with "white light" (the whole spectrum) as it passes through the material (lens in our case).. the "blue" is refracted more then "red" waves and the light is broken into it's component colors (dispersion).. The result is "chromatic aberrations" .
    Abbe number is the measurement of the material to break white light into its component colors, the "image" formed by blue rays is a different distance from the lens then the image formed by red waves etc. etc... result?.. Those nasty "rainbows" you see or color fringes along letters etc. etc.
    To come up with the abbe number you need to know the index of refraction for several different wavelengths. In the US (standard) we use yellow(588nm) Blue (486) red (656)
    The formula is nyellow-1 over nblue-nred

    So back to the original, index of refraction, I'm sure you heard that one before, but most people don't figure into it that you use the speed of yellow wave (588) for the index of refraction :)
    The amount of refraction (or bending) by any material is based on the speed of light through the material. The more the ray is slowed the more it is refracted. The higher the index of refraction the slower the light travels through the material, and the more it "bends".. this is the reason a higher index lens are thinner than lower indexed lens even of the same power :) .. the material slows the light more, so the curve on the lens bends the light more then the same curve would do on a lower indexed lens :)Hey maybe I should try to turn this in as a xtra credit for school That is after I have been corrected by these other lens guru's and they straighten out this lowly lab rat :)

    Jeff "this is my story and I'm sticking to it" Trail



  3. #3
    Master OptiBoarder Darryl Meister's Avatar
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    Hi Pete,

    Jeff nicely described how chromatic aberration affects light, as well as how it is measured. The issue of "why" lens materials slow down and disperse light is another story, however...

    Transparent lens materials slow and disperse white light. Essentially, the outermost atoms of a transparent lens material absorb incident radiation (i.e., light). The atoms then re-emit the radiation into adjacent atoms, and the process continues until the radiation propogates through the material. The slight time delay between the absorption and re-emission of the radiation by the atoms is what causes the light to "slow down." The ratio of the velocity of light in free space to the reduced velocity of light in a transparent material is referred to as the index of refaction of the lens material.

    Moreover, transparent materials have "resonant frequencies" in the ultraviolet radiation end of the electromagnetic radiation spectrum. Because of this, the atoms "hold on" to the UV radiation and convert much of this energy into heat. This is also why transparent lens materials absorb most UV radiation. Violet and blue visible radiation, adjacent to the ultraviolet radiation, are still "held on" to because their frequencies are close to the resonant frequency. However, they are not held as long as the UV radiation and are also not absorbed as much UV. Consequently, colors near the UV end of the spectrum (such as blue and violet) travel more slowly through the transparent material than colors at the red end. This is what causes chromatic dispersion: Different colors of light have different velocities. This also means that each color of light has its own index of refraction; blue light has a higher index than red light.

    High-index lens materials generally don't refract light as efficiently as crown glass and CR-39. These materials have greater differences between the velocities of blue and red light.

    As Jeff pointed out, the "stated" refractive index of a lens material is simply the single index of refraction of a particular color that represents the average color of the visible spectrum (this yellow-green color is produced by the helium d line for measurement purposes).

    Best regards,
    Darryl

  4. #4
    sub specie aeternitatis Pete Hanlin's Avatar
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    Thanks for the explanations... I was already familiar with the varying speeds between light of differing wavelengths and the calculation of Abbe Value (in fact, if I'm not mistaken, there are countries which employ a slightly different reference wavelength for determining power and index), but the resonant frequencies and discussion of atoms was new to me. When I'm teaching the mechanics of refraction, I use an illustration of a ruler (representing a wavefront) falling into a body of water. If the ruler strikes the water obliquely, one end of the ruler slows down slightly before the other (thus changing the direction of the ruler's path).

    So am I to interpret Darryl's answer to mean that the "resonant frequency" of a lens determines its tendancy to refract shorter wavelengths more or less than longer wavelengths? Does this have any relation to the "black lines" on the spectrum exhibited by light cast from different light sources (e.g., argon, sodium, etc.)?

    Also, going back to a discussion we had some time ago (determining index of refraction using unconventional means), couldn't you use an extremely sensitive thermometer and a UV light to determine index of refraction (measuring the heat being absorbed into the material)?

    Pete

  5. #5
    Master OptiBoarder Darryl Meister's Avatar
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    Hi Pete,

    The resonant frequency applies to the electrons of the atoms within the material. This is related Fraunhofer bright/dark lines -- but not the cause. These lines represent the colors produced by certain elements when their atoms are "excited." When an atom, of say hydrogen or some other element, aborbs a certain level of energy an electron orbiting the nucleus of the atom is excited to a different level (i.e., "quantum" level). When the electron drops back to its lower state it emits the same level of energy. Each level of energy corresponds to a specific frequency (color) of light.

    I think that it would be best if you simply stated that the resonant frequency of the atoms within a lens material lies beyond the blue end of the visible spectrum, which causes the material to slow down blue light more than red light.

    It would be difficult -- if not impossible -- to measure the refractive index of a material using a thermometer. The change in the temperature of the lens would probably be very slight, and will depend upon the nature of the lens material, lens thickness, etcetera.

    Yes, some countries -- like Germany and Japan -- use a different color to measure the refractive index (corresponding to the mercury e line (at 546.1 nm) -- see my earlier paragraph on Fraunhofer lines). This color is slightly more towards the blue end of the spectrum than the helium d line (at 587.6 nm) used in the United States.

    I generally describe refraction with an analogy to driving... When your car drives off the smooth highway and into the rough shoulder off the road, the shoulder slows down the left side of your car and causes it to "pull" to the left. This is similar to what happens to light striking a material that resists its speed at an angle.

    Best regards,
    Darryl

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    Objection! OptiBoard Gold Supporter shanbaum's Avatar
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    Confused

    Originally posted by Darryl Meister:
    I generally describe refraction with an analogy to driving... When your car drives off the smooth highway and into the rough shoulder off the road, the shoulder slows down the left side of your car and causes it to "pull" to the left. This is similar to what happens to light striking a material that resists its speed at an angle.
    ...assuming that you're a) lucky enough to make it through the oncoming traffic, or b) in the U.K., Japan, Australia, Bermuda, Thailand, or South Africa (did I miss anyone?), or c) driving in reverse.


  7. #7
    Master OptiBoarder Darryl Meister's Avatar
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    Originally posted by shanbaum:
    ...assuming that you're a) lucky enough to make it through the oncoming traffic, or b) in the U.K., Japan, Australia, Bermuda, Thailand, or South Africa (did I miss anyone?), or c) driving in reverse.
    Good point... I actually meant my "other left." ;)

    Best regards,
    Darryl

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    opti-tipster harry a saake's Avatar
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    Redhot Jumper

    Hello Darryl, nice post, curious as how do the atoms reemit, by sending out other atoms?,also you mentioned reasonant frequencies, i,m curious as to what the actual freq. is, megacycles or megahertz, your choice. Also by reemitting, would this not also cause a certain amount of loss of light?

  9. #9
    Master OptiBoarder Darryl Meister's Avatar
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    Hi Harry,

    The atoms don't re-emit other atoms, they re-emit photons. Photons of light contain energy (proportional to the frequency of light). When a photon is absorbed by an atom, the energy is used to excite one of the electrons orbiting the atom to a higher energy level, farther away from the nucleus. (The electron is attracted to the nucleus of the atom, so increasing the distance from the nucleus increases the potential energy between them.) When the electron drops back to a lower level, it releases energy in the form of a photon. Consequently, an atom can absorb this energy and then re-emit it on to other atoms.

    There may be some light loss, depending upon the interaction between light and the lens material (e.g., tinted lenses).

    I don't know that anyone actually measures the resonant frequency of the lens material in our industry. If it falls within the UV region though, the wavelength must lie below 380 nm (which I believe would be a frequency of 7.9 x 10^13 Hertz).

    Best regards,
    Darryl

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