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Physics II

The Simple Magnifier. What do we do with an object when we really want to look at it closely?We bring it up as close to our eye as possible.In this way light from it illuminates as large an area on our retina as possibleMore receptors activated implies more detail seenOf course we are limited as

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Physics II

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    1. Physics II Microscopy Title PageTitle Page

    2. The Simple Magnifier What do we do with an object when we really want to look at it closely? We bring it up as close to our eye as possible. In this way light from it illuminates as large an area on our retina as possible More receptors activated implies more detail seen Of course we are limited as to how close we can bring object by the accomodation limits of our eyes Simple Magnifier PrinciplesSimple Magnifier Principles

    3. Angular magnification A.k.a. magnifying power MA = ?a/ ?u . ?a is (aided) angle subtended at eye by image at eye when magnifier is used ?u is angle (unaided) angle subtended by image at eye when magnifier is NOT used. Angular magnificationAngular magnification

    4. Fooling the eye again We can use a positive (convex) lens to form an image at the near point or “at infinity” that will subtend the same angle as at the close distance. Fooling the eye againFooling the eye again

    5. Ray Diagram Ray diagram for virtual image in + lens Ray diagram for positive lensRay diagram for positive lens

    6. Mathematics The angle ? subtended at the lens by the object (angle OCO’) equals the angle subtended by the image (angle ICI’) The Gauss thin lens equation insists that 1/ so + 1/ si = 1/ f Geometry ?u = yo / dn ?o = yo / so MathematicsMathematics

    7. Result MA = ?a / ?u . MA= dn / so . MA= dn x (1 / f - 1 / si ) If the eye is relaxed si is “- infinity” MA= dn / f If maximum accommodation is used then Si = - dn . MA = dn / f + 1 Angular magnification of simple magnifier in two simple cases.Angular magnification of simple magnifier in two simple cases.

    8. The convention By convention the near point distance is that of 40 year old males dn = 25.4 cm or 25 cm MA = 25.4 / f or 25 / f when we measure f in centimeters. (Image at infinity) MA = 25.4 / f + 1 or 25 / f + 1 (max. magnification) The conventional numbersThe conventional numbers

    9. Two-lens systems Optical systems such as telescopes and microscopes are often modeled as two- lens systems. The lens (or mirror) that collects the light from the object is called the objective. The eyepiece (ocular) is a lens or a collection of lenses which is used to view the image formed by the objective. Even the collection is modeled as a single lens. Two- lens systems.Two- lens systems.

    10. Details of Two lens System Hecht develops the arithmetic of the two lens system in Example 24.8 in both versions of the textbook. si1 =(f2d-f2[so1f1/(so1-f1)])/(d – f2 –[s01f1/(so1-f1)]) d is here the distance between the center planes of the lenses d = f1 + L + f2 L is called the “optical tube length” DetailsDetails

    11. Applied two lens systems. But here we look at the two most common “special cases” of the two-lens system—the telescope and the microscope Lens 1 (the lens that the light penetrates first) is called the “objective lens” Lens 2 (the lens that the light strikes second) is called the “eyepiece” or “ocular” It is generally a set of 3 or more lenses here replaced by a single equivalent thin lens. The many lens version corrects for various abberrations we are ignoring here. Applied two-lens systems.Applied two-lens systems.

    12. Notation redux yo1 = height of object s01 = distance of object from objective yi1 = height of intermediate image yo2 = height of intermediate image acting as object for ocular = yi1 si1 = distance of intermediate image from objective lens so2 = distance of intermediate image from ocular si2 = final image distance from ocular Notation collected and summarized.Notation collected and summarized.

    13. Notation continued fO = f1 = focal length of objective fE = f2 = focal length of eyepiece d = distance from ocular to object L = “optical tube length” = distance between second principal focus of objective and 1st principal focus of ocular (2nd principal focus in case of Galilean telescope) MTO = transverse magnification of objective lens MTE = transverse magnification of ocular MA = angular magnification of system Notation continuedNotation continued

    14. Compute angular magnification MA = ?a / ?u In the small angle, paraxial ray approx. ?u = yo1 / d ?a = yi2 / si2 . MA = (yi2 / si2 ) / (yo1 / d) = (yi2/yo2)(yo2/yo1)(d/si2) = (yi2/yo2)(yi1/yo1)(d/si2)= (-(si2/so2))(-si1/so1))(d/si2) = MTOMTE (d / si2) MA = (d si1) / (so2 so1) The final “image distance” has “canceled out.” Compute the general angular magnification in small angle, thin lens approximationCompute the general angular magnification in small angle, thin lens approximation

    15. Telescopes Keplerian (astronomical) telescope Both ocular and objective lenses are positive Final image is “inverted” Intermediate image formed very near 2nd principal focal point of the objective and 1st principal focal point of the ocular Galilean (terrestrial) telescope Objective is positive , ocular negative Final image is “erect.” TelescopesTelescopes

    16. Telescope approximations MA = (d si1) / (so2 so1) d = so1 . si1 = fO so2 = fE MA = fO / fE. = DE / DO For large magnification, low power objective and high power objectives are desired. For the telescopeFor the telescope

    17. Microscope Approximations MA = (d si1) / (so2 so1) d = L Si1 = L So1 = fO So2 = fE MA = L2/(fOfE) = DODE L2 . The “optical tube length” L is usually set by manufacturers at 16 cm. For large magnification use high power objectives and oculars. Microscope ApproximationsMicroscope Approximations

    18. Web Resources http://micro.magnet.fsu.edu/primer/index.html (tutorial primer) http://micro.magnet.fsu.edu/primer/anatomy/anatomyjava.html Interactive Java tutorials http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/cirapp2.html#c2 (Airy’s disk Web Resources re microscopyWeb Resources re microscopy

    19. Hecht’s formula Hecht’s formula differs a little bit from ours He has used slightly different approximations. MA = Ldn / (fOfE) = 160 mm x 254 mm / (fOfE) The main point is that the magnification is proportional to the product of the lens powers in both formulations. Hecht’s formulaHecht’s formula

    20. Other considerations Other important considerations in microscopy Resolution Depth of field Contrast Parfocal Field of view Brightness of image Other important considerations in biological microscopy.Other important considerations in biological microscopy.

    21. Contrast Biological specimens of often difficult to view because the difference in contrast between various parts of the specimen is very low. Several inventions serve to increase that contrast. Phase contrast microscopy Confocal Microscopy Multiple-photon microscopy These last two also serve to increase the depth of field. ContrastContrast

    22. Phase Contrast Microscopes Java Applet tutorial on phase contrast Tutorial Uses diffraction (i.e. wave properties) of light to enhance contrast in unstained specimens. Phase Contrast (Zernike) microscopyPhase Contrast (Zernike) microscopy

    23. Confocal Microscopes Tutorial on laser-scanning confocal microscopes Several proposals at EPSCoR presentation involved obtaining confocal and two-photon microscopes for Oklahoma facilities. Confocal MicroscopyConfocal Microscopy

    24. Resolving Power Refers to the ability to distinguish between two distinct images and a single image Confusion occurs because of diffraction as light passes through the circular aperture of the objective lens. Points image as disk with concentric rings Airy disk. Resolving PowerResolving Power

    25. Airy Disk Image The Airy Disk. Image of Airy Disk.Image of Airy Disk.

    26. Rayleigh Criterion Lord Rayleigh (John William Strutt) enunciated a resolution criterion Two objects can be discerned as separate when the central diffraction maximum of one lies on the first diffraction minimum of the second. ?a = 1.22 ? / D (radians) As in golf, the smaller, the better. The Rayleigh CriterionThe Rayleigh Criterion

    27. More detail The definition of the limit of resolution in a microscope is often given in terms of the numerical aperture N.A. = nsin? Java Applet for resolving power ?a = 1.22 ?o / (nD) ?o= wavelength in vacuo More than you wanted to know.More than you wanted to know.

    28. Parfocal The Parfocal property is the property of microscopes that relates to the amount of readjustment needed when the observer switches between low and high magnification and vice versa. Generally refers to sets of eyepieces having coinciding focal points ParfocalParfocal

    29. Field of View Interactive Tutorial http://www.microscopyu.com/tutorials/java/fielddiameter/index.html The field of view (a.k.a. field number) is the linear size (in millimeters) of the intermediate image. Field number as large as 28 mm possible Field size in specimen plane = field number / MTO Field of ViewField of View

    30. Image Brightness Web resource http://micro.magnet.fsu.edu/primer/anatomy/imagebrightness.html Image brightness is proportional to the square of the numerical aperture of the objective and inversely proportional to the square of the linear magnification of the objective Image Brightness is proportional to (NA/MTO)2 Image brightnessImage brightness

    31. Two-Photon microscopy Tutorial Another Tutorial Two-Photon MicroscopyTwo-Photon Microscopy

    32. More Fun yet Atomic Force Microscopy Another Tutorial Atomic Force MicroscopyAtomic Force Microscopy

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