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Chapter 33 Lenses and Op/cal Instruments
Units of Chapter 33 Telescopes Compound Microscope Aberrations of Lenses and Mirrors
33-2 The Thin Lens Equation; Magnification The thin lens equation is similar to the mirror equation: 1 d 0 + 1 d i = 1 f
33-2 The Thin Lens Equation; Magnification The sign conventions are slightly different: 1. The focal length is positive for converging lenses and negative for diverging. 2. The object distance is positive when the object is on the same side as the light entering the lens (not an issue except in compound systems); otherwise it is negative. 3. The image distance is positive if the image is on the opposite side from the light entering the lens; otherwise it is negative. 4. The height of the image is positive if the image is upright and negative otherwise.
33-2 The Thin Lens Equation; Magnification The magnification formula is also the same as that for a mirror: m = h i h 0 = d i d 0 The power of a lens is positive if it is converging and negative if it is diverging.
33-4 Lensmaker s Equation This useful equation relates the radii of curvature of the two lens surfaces, and the index of refraction, to the focal length:
33-7 Magnifying Glass The closest distance at which a normal eye can focus clearly is called the near point of the eye (which is in average 25 cm). If instead the lens is held such that the image is at the near point of the eye (25 cm), a larger angular magnification can be obtained. If the lens is held such that its front focal point is on the object being viewed, the relaxed eye can view the image with angular magnification Angular magnifica/on or magnifying power M = tan θ tanθ θ θ = h f h N = N f
33-7 Magnifying Glass The power of a magnifying glass is described by its angular magnification: If the eye is relaxed (N is the near point distance and f the focal length): If the eye is focused at the near point:
33-8 Telescopes Refracting type The objective lens form a real image (I 1 ) The eyepiece acts as magnifier. It produces a second image (I 2 ), which is virtual and inverted.
Refrac/ng Telescope M θ θ = h f e h f 0 = f 0 f e
33-8 Telescopes A refracting telescope consists of two lenses at opposite ends of a long tube. The objective lens is closest to the object, and the eyepiece is closest to the eye. The magnification is given by
33-8 Telescopes Astronomical telescopes need to gather as much light as possible, meaning that the objective must be as large as possible. Hence, mirrors are used instead of lenses, as they can be made much larger and with more precision.
Reflec/ng Telescope
Reflec/ng Telescope: Hubble Telescope
Reflec/ng Telescope The largest LMT on Earth is the Large Zenith Telescope in British Columbia. Its spinning liquid mirror is almost 6 m across and weighs three tons, making it the third-largest telescope in North America.
33-8 Telescopes A terrestrial telescope, used for viewing objects on Earth, should produce an upright image. Here are two models, a Galilean type and a spyglass:
33-9 Compound Microscope A compound microscope also has an objective and an eyepiece; it is different from a telescope in that the object is placed very close to the eyepiece.
33-9 Compound Microscope The magnification is given by
33-10 Aberrations Lenses do not form perfect images. There is always some degree of distortion (so-called aberration) introduced by the lens that causes the image to be an imperfect replica of the object.
Dispersion causes Chromatic Aberration The spreading of white light into the full spectrum is called dispersion. White light is a mixture of all visible wavelengths, and when incident on a prism the different wavelengths are bent to varying degrees. Because the index of refraction is greater for shorter wavelengths
Chromatic Aberrations Chromatic aberration is caused by the dispersion of the lens material (the variation of its refractive index, n, with the wavelength of light). Since the focal length f is dependent upon n, it follows that different wavelengths of light will be focused to different positions.
Chromatic Aberrations
Chromatic Aberrations On top is corner detail in a photograph taken with a higher quality lens; bo:om is a similar photograph taken with a wide angle lens showing severe visible chroma=c aberra=on, the effect is pronounced on the right side of the building's roof, where a long blue streak is visible
Chromatic Aberrations
Achromatic Doublet The most common type of achromatic lens is the achromatic doublet, which is composed of two individual lenses made from glasses with different amounts of dispersion. Usually one element is a concave lens made out of flint glass, which has relatively high dispersion, while the other, convex, element is made of crown glass, which has lower dispersion; other low dispersion glasses may be used instead. The lens elements are mounted next to each other, often cemented together, and shaped so that the chromatic aberration of one is counterbalanced by that of the other.
Achromatic Lens
Spherical Aberrations Spherical aberration occurs because spherical surfaces are not the ideal shape with which to make a lens, but they are by far the simplest shape to which glass can be ground and polished and so are often used. Spherical aberration causes beams parallel to (but distant from) the lens axis to be focused in a slightly different place than beams close to the axis. This manifests itself as a blurring of the image.
Spherical Aberrations Spherical aberra=on causes beams parallel to (but distant from) the lens axis to be focused in a slightly different place than beams close to the axis. This manifests itself as a blurring of the image.
Spherical Aberrations A point source as imaged by a system with spherical aberration.
Spherical Aberrations A point source as imaged by a system with spherical aberra=on nega/ve (top) means peripheral rays are not bent enough, zero (centre) so- called circle of least confusion, and posi/ve (bo:om) means peripheral rays are bent too much. Images to the lek are defocused toward the inside, images on the right toward the outside
Spherical Aberrations
Aspheric Lens An aspheric lens or asphere is a lens whose surface profiles are not portions of a sphere or cylinder. The asphere's more complex surface profile can reduce or eliminate spherical aberration.
Comatic Aberrations Coma, which derives its name from the comet- like appearance of the aberrated image, occurs when an object off the op=cal axis of the lens is imaged, where rays pass through the lens at an angle to the axis θ. Rays that pass through the centre of the lens of focal length f are focused at a point with distance- - f tan θ- - from the axis. Rays passing through the outer margins of the lens are focused at different points
Coma/c Aberra/ons
Waves as Rays Diffrac/on can not be explained within the ray approxima/on
Ray optics is the limit of wave optics when the wavelength is infinitesimally short, λ 0 As long as the light waves propagate through and around objects whose dimensions are much greater than the wavelength, ray optics suffices for describing most optical phenomena.
Chapter 34 The Wave Nature of Light; Interference
Units of Chapter 34 Waves versus Particles; Huygens Principle and Diffraction Huygens Principle and the Law of Refraction Interference Young s Double-Slit Experiment
34-1 Waves versus Particles; Huygens Principle and Diffraction Huygens principle: every point on a wave front acts as a point source; the wave front as it develops is tangent to all the wavelets.
34-1 Waves versus Particles; Huygens Principle and Diffraction Huygens principle is consistent with diffraction:
34-2 Huygens Principle and the Law of Refraction Huygens principle can also explain the law of refraction. As the wavelets propagate from each point, they propagate more slowly in the medium of higher index of refraction. This leads to a bend in the wave front and therefore in the ray.
34-2 Huygens Principle and the Law of Refraction
34-2 Huygens Principle and the Law of Refraction Highway mirages are due to a gradually changing index of refraction in heated air.
34-3 Interference Young s Double-Slit Experiment If light is a wave, interference effects will be seen, where one part of a wave front can interact with another part, as in the double-slit experiment:
34-3 Interference Young s Double-Slit Experiment If light is a wave, there should be an interference pattern.
Double- Slit Experiment destruc/ve interference construc/ve interference
34-3 Interference Young s Double-Slit Experiment The interference occurs because each point on the screen is not the same distance from both slits. Depending on the path length difference, the wave can interfere constructively (bright spot) or destructively (dark spot).
34-3 Interference Young s Double-Slit Experiment d sinθ = mλ m = 0,1,2,... Construc/ve interference d sinθ = (m + 1 )λ m = 0,1,2,... 2 Destruc/ve interference