Thursday, July 13, 2006

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Chapter 27:  Optical Instruments

27-1:  The Human Eye and the Camera
    The human eye and a camera both form a real, inverted image that is focused either on the retina or photographic film.
    The eye is focused by the ciliary muscles, which change the shape of the lens (accommodation).
    A camera is focused by moving the lens (with fixed focal length) closer or farther from the film.
    The near point is the closest distance from the eye that a person can focus.  Typical value:  N ~ 25 cm ~ 10 in.
    The far point is the greatest distance from the eye that a person can focus.  For a normal eye, the far point is infinity.
    The f-number of a lens relates the diameter of the aperture, D, to the focal length, f.  f-number = f/D

27-2:  Lenses in Combination and Corrective Optics
    When lenses are used in combination, the image produced by one lens acts as the object for the next lens.
    The total magnification of a system of lenses is the product of the magnifications produced by each individual lens.
    Nearsightedness is a condition where a person can only focus on objects that are near (not at infinity), often caused by an elongation of the eyeball (prolate spheroid) so that the image forms in front of the retina.  Nearsightedness can be corrected by placing a diverging lens in front of the eye to extend the focal range of the eye.
    Farsightedness is a condition where a person can only focus on objects that are far away, so that the near point is significantly greater than the usual 25 cm.  This condition tends to occur in most humans as they get older, sometimes cause by a shortening of the eyeball (oblate spheroid) or weakened ciliary muscles so that the image forms behind the retina.  Farsightedness can be corrected by placing a converging lens in front of the eye to shorten the focal range of the eye.
    Ponderable:  What is the near point for a typical person with myopia?
    Ponderable:  What is wrong with the following statement?  "My aunt is far sighted with a far point of about 5.0 m."
    The refractive power of a lens is a measure of the ability of a lens to bend light and is measured in diopters (1/m):  refractive power = 1/f, where f is in meters.
       As is the case for focal lengths, a positive refractive power indicates a converging lens, while negative indicates a diverging lens.

27-3:  The Magnifying Glass
    A magnifying glass is simply a converging lens held in front of the eye to produce an enlarged virtual image of an object that is closer than the near-point distance, thereby resulting in an increased angular size.
    Magnification:  M = N/f (image at infinity) or  M = 1 + N/f  (image at near point)
    T/F:  A magnifying glass produces an image that is closer than the near point.

27-4:  The Compound Microscope
    A compound microscope uses two lenses in combination (an objective and an eyepiece) to produce a magnified image.
    The object to be viewed is placed just beyond the focal length of the objective.  The image formed by the objective is then viewed by the eyepiece to yield an increased magnification:  M = -di*N/(fobjective*feyepiece)

27-5:  Telescopes
    A telescope produces magnified views of distant objects using two lenses or mirrors.  The objective lens or mirror focuses incoming light to its focal point (since the objects are very far away), and the eyepiece magnifies the image formed by the objective.
    The total magnification is:  M = fobjective/feyepiece
    The length of a Galilean telesope is L = fobjective + feyepiece, but this length can be reduced by "folding" the light path, as is the case for most large telescopes and many telescopes used by amateur astronomers.

27-6:  Lens Aberrations
    Any deviation of a lens from ideal behavior is referred to as an aberration.
    Spherical aberration results from light passing through different parts of a lens not passing through a single focal point.  This aberration can be reduced by limiting the aperture size or using an aspherical lens that is specially shaped to avoid this problem.
    Chromatic aberration results from dispersion within a refracting material, so that different colors of light focus at different points.  Achromatic lenses are made to correct this problem by combining two or more lenses with different refractive properties.

Concept Tests