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- Refractive Optics Chapter 26
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- Refractive Optics Refraction Refractive Image Formation Optical Aberrations The Human Eye Optical Instruments
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- Refraction Refractive Index Snells Law Total Internal Reflection Polarization Longitudinal Focus Shift Dispersion
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- Refraction: Refractive Index Speed of light in vacuum: c = 3.0010 8 m/s Speed of light in anything but vacuum: < c Index of refraction: n is a dimensionless ratio 1
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- Refraction: Refractive Index Index of refraction: n depends on: material wavelength of light
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- Refraction: Snells Law When light passes from one material into another:
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- Refraction: Snells Law When light passes from a less-dense (lower index) medium into a more-dense (higher index) medium, the light bends closer to the surface normal.
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- Refraction: Snells Law
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- Snells Law: Total Internal Reflection Consider light passing from a more-dense medium into a less-dense one (example: from water into air). The angle of refraction is larger than the angle of incidence.
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- Snells Law: Total Internal Reflection If the angle of incidence is large enough, the angle of refraction increases to 90 n = n 2 n = n 1
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- Snells Law: Total Internal Reflection At that point, none of the light is transmitted through the surface. All of the light is reflected (total internal reflection). The angle of incidence for which this happens is called the critical angle. n = n 2 n = n 1
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- Snells Law: Total Internal Reflection We can easily calculate the critical angle by imposing the additional condition on Snells Law:
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- Snells Law: Polarization We can calculate the angle of incidence for light entering a more-dense medium from a less-dense medium so that the reflected and refracted rays are perpendicular: n = n 2 n = n 1
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- Snells Law: Polarization By inspection of our drawing, we see that the perpendicularity of the reflected and transmitted rays requires that: n = n 1 n = n 2
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- Snells Law: Polarization Snells Law: Substitute for 2 :
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- Snells Law: Polarization Snells Law: Substitute for 2 : angle-difference identity:
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- Snells Law: Polarization B is called Brewsters angle.
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- Snells Law: Polarization When light is incident on a dielectric at Brewsters angle: the reflected light is linearly polarized, perpendicular to the plane of incidence the transmitted light is partially polarized, parallel to the plane of incidence n = n 1 n = n 2
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- Snells Law: Longitudinal Focus Shift Rays are converging to form an image:
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- Snells Law: Longitudinal Focus Shift Insert a window: the focus is shifted rightward (delayed)
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- Snells Law: Longitudinal Focus Shift The amount of the longitudinal focus shift:
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- Snells Law: Longitudinal Focus Shift If an object is immersed in one material and viewed from another: apparent depth
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- Snells Law: Longitudinal Focus Shift The longitudinal focus shift and apparent depth relationships presented: are paraxial approximations. Even flat surfaces exhibit spherical aberration in converging or diverging beams of light.
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- Snells Law: Dispersion As we noted earlier, the index of refraction depends on: the material the wavelength of the light The dependence of refractive index on wavelength is called refractive dispersion.
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- Snells Law: Dispersion If each wavelength (color) has a different value of n, applying Snells law will give different angles of refraction for a common angle of incidence.
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- Refractive Image Formation: Lenses Just as we used curved (spherical) mirrors to form images, we can also use windows with curved (spherical) surfaces to form images. Such windows are called lenses. A lens is a piece of a transmissive material having one or both faces curved for image-producing purposes. (A lens can also be a collection of such pieces.)
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- Refractive Image Formation: Lenses Lens forms (edge views) Positive: center thicker than edge Negative: edge thicker than center
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- Refractive Image Formation: Lenses Positive: also called converging Negative: also called diverging
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- Refractive Image Formation: Lenses Real image formation by a positive lens:
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- Refractive Image Formation: Lenses Positive lens, d o > 2f:
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- Refractive Image Formation: Lenses Positive lens, d o = 2f:
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- Refractive Image Formation: Lenses Positive lens, f < d o < 2f:
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- Refractive Image Formation: Lenses Positive lens, d o = f:
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- Refractive Image Formation: Lenses Positive lens, d o < f:
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- Refractive Image Formation: Lenses Negative lens, d o >> f:
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- Refractive Image Formation: Lenses Negative lens, d o > f:
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- Refractive Image Formation: Lenses Negative lens, d o < f:
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- Refractive Image Formation: Lenses How are the conjugate distances measured? Thin lens: a simplifying assumption that all the refraction takes place at a plane in the center of the lens.
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- Refractive Image Formation: Lenses A better picture: thick lens: The conjugate distances are measured from the principal points.
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- Refractive Image Formation: Lenses A catalog example: Image from catalog of Melles Griot Corporation
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- Refractive Image Formation: Lenses The lens equation: Magnification: Combinations: one lenss image is the next lenss object.
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- Refractive Image Formation: Lenses Sign conventions Light travels from left to right Focal length: positive for a converging lens; negative for diverging Object distance: positive for object to left of lens (upstream); negative for (virtual) object to right of lens Image distance: positive for real image formed to right of lens from real object; negative for virtual image formed to left of lens from real object Magnification: positive for image upright relative to object; negative for image inverted relative to object
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- Aberrations Image imperfections due to surface shapes and material properties. Not (necessarily) caused by manufacturing defects. A perfectly-made lens will still exhibit aberrations, depending on its shape, material, and how it is used.
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- Aberrations The basic optical aberrations Spherical aberration: the variation of focal length with ray height Coma: the variation of magnification with ray height Astigmatism: the variation of focal length with meridian Distortion: the variation of magnification with field angle Chromatic: the variation of focal length and/or magnification with wavelength (color)
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- Lens Power The reciprocal of the focal length of a lens is called its power. This isnt power in the work-and-energy sense. It really means the efficacy of the lens in converging rays to focus at an image. It can be positive or negative. If thin lenses are in contact, their powers may be added. Unit: if the focal length is expressed in meters, the power is in diopters (m -1 ).
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- The Human Eye Horizontal section of right eyeball (as seen from above). Illustration taken from Warren J. Smith, Modern Optical Engineering, McGraw-Hill, 1966)
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- The Human Eye Characteristics Field of view (single eye): 130 high by 200 wide Field of view both eyes simultaneously: 130 diameter Visual acuity (resolution): 1 arc minute Vernier acuity: 10 arc seconds accuracy; 5 arc seconds repeatability Spectral response: peaks at about = 0.55 m (yellow- green). Response curve closely matches solar spectrum. Pupil diameter: ranges from about 2 mm (very bright conditions) to about 8 mm (darkness).
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- The Human Eye Function Image distance is nearly fixed (determined by eyeball shape and dimensions Viewing objects significantly closer than infinity: accommodation Far point: the farthest-away location at which the relaxed eye produces a focused image (normally infinity) Near point: the closest location at which the eyes ability to accommodate can produce a focused image (normal near point is 25 cm for young adults)
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- The Human Eye Defects and Problems Myopia (nearsightedness) Too much power in cornea and lens (or eyeball too long) Far point is significantly closer than infinity Corrected with diverging lens (negative power)
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- The Human Eye Defects
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