Chapter 25 Optical Instruments 2010 11 30 Optical
- Slides: 46
Chapter 25 Optical Instruments 2010 -11 -30
Optical Instrument n n n It generally involves the laws of reflection and refraction It uses the procedures of geometric optics For certain phenomena, the wave nature of light must be used
The Camera n n The single-lens photographic camera is an optical instrument Components n n Light-tight box Converging lens n n Produces a real image Sensor behind the lens receives the inverted image
Camera Operation n Proper focusing leads to sharp images n n n The lens-to-sensor distance will depend on the object distance and on the focal length of the lens The shutter is a mechanical device that is opened for selected time intervals Most cameras have an aperture of adjustable diameter to further control the intensity of the light reaching the film n With a small-diameter aperture, only light from the central portion reaches the film, and spherical aberration is minimized
Camera Operation, Intensity n Light intensity is a measure of the rate at which energy is received by the sensor per unit area of the image n n The intensity of the light reaching the sensor is proportional to the area of the lens The brightness of the image formed on the sensor depends on the light intensity n Depends on both the focal length and the diameter of the lens
Camera, f-numbers n The ƒ-number of a camera is the ratio of the focal length of the lens to its diameter n ƒ-number = f/D f/4
f-number f/3 f/16 Large f-number, or small lens dia.
The Eye – a biological camera n n The normal eye focuses light and produces a sharp image Essential parts of the eye n n Cornea – light passes through this transparent structure Aqueous Humor – clear liquid behind the cornea
The Eye – Operation n The cornea-lens system focuses light onto the back surface of the eye n n n This back surface is called the retina The retina contains receptors called rods and cones These structures send impulses via the optic nerve to the brain n The brain converts these impulses into our conscious view of the world
The Eye – muscle focusing n The eye can focus on a distant object n n The ciliary muscle is relaxed The zonules tighten This causes the lens to flatten, increasing its focal length For an object at infinity, the focal length of the eye is equal to the fixed distance between lens and retina n This is about 1. 7 cm
The Eye – Focusing, cont n The eye can focus on near objects n n The ciliary muscles tenses This relaxes the zonules The lens bulges a bit and the focal length decreases The image is focused on the retina
The Eye – Near and Far Points n The near point is the closest distance for which the lens can accommodate to focus light on the retina n n n Typically at age 10, this is about 18 cm It increases with age The far point of the eye represents the largest distance for which the lens of the relaxed eye can focus light on the retina n Normal vision has a far point of infinity
Conditions of the Eye n n Eyes may suffer a mismatch between the focusing power of the lens-cornea system and the length of the eye Eyes may be n Far-sighted n n Light rays reach the retina before they converge to form an image Near-sighted n Person can focus on nearby objects but not those far away
Far-sightedness n n n Also called hyperopia The image focuses behind the retina Can usually see far away objects clearly, but not nearby objects
Correcting Farsightedness n n A converging lens placed in front of the eye can correct the condition The lens refracts the incoming rays more toward the principle axis before entering the eye n This allows the rays to converge and focus on the retina
Near-sightedness n n n Also called myopia In axial myopia the nearsightedness is caused by the lens being too far from the retina In refractive myopia, the lens-cornea system is too powerful for the normal length of the eye
Correcting Nearsightedness n n A diverging lens can be used to correct the condition The lens refracts the rays away from the principle axis before they enter the eye n This allows the rays to focus on the retina
Simple Magnifier n n n A simple magnifier consists of a single converging lens This device is used to increase the apparent size of an object The size of an image formed on the retina depends on the angle subtended by the eye
The Size of a Magnified Image n When an object is placed at the near point, the angle subtended is a maximum n n The near point is about 25 cm When the object is placed near the focal point of a converging lens, the lens forms a virtual, upright, and enlarged image
Angular Magnification n n Angular magnification is defined as The angular magnification is at a maximum when the image formed by the lens is at the near point of the eye n n q = - 25 cm Calculated by
Magnification by a Lens n n With a single lens, it is possible to achieve angular magnification up to about 4 without serious aberrations With multiple lenses, magnifications of up to about 20 can be achieved n The multiple lenses can correct for aberrations
Compound Microscope n A compound microscope consists of two lenses n n n Gives greater magnification than a single lens The objective lens has a short focal length, ƒo<1 cm The ocular lens (eyepiece) has a focal length, ƒe, of a few cm
Compound Microscope, cont n The lenses are separated by a distance L n n The approach to analysis is the same as for any two lenses in a row n n L is much greater than either focal length The image formed by the first lens becomes the object for the second lens The image seen by the eye, I 2, is virtual, inverted and very much enlarged
Magnifications of the Compound Microscope n n n The lateral magnification of the microscope is The angular magnification of the eyepiece of the microscope is The overall magnification of the microscope is the product of the individual magnifications
Other Considerations with a Microscope n The ability of an optical microscope to view an object depends on the size of the object relative to the wavelength of the light used to observe it n For example, you could not observe an atom (d 0. 1 nm) with visible light (λ 500 nm)
Telescopes n Two fundamental types of telescopes n n n Refracting telescope uses a combination of lenses to form an image Reflecting telescope uses a curved mirror and a lens to form an image Telescopes can be analyzed by considering them to be two optical elements in a row n The image of the first element becomes the object of the second element
Refracting Telescope n n The two lenses are arranged so that the objective forms a real, inverted image of a distant object The image is near the focal point of the eyepiece The two lenses are separated by the distance ƒo + ƒe which corresponds to the length of the tube The eyepiece forms an enlarged, inverted image of the first image
Angular Magnification of a Telescope n n The angular magnification depends on the focal lengths of the objective and eyepiece Angular magnification is particularly important for observing nearby objects n Very distant objects still appear as a small point of light
Disadvantages of Refracting Telescopes n n n Large diameters are needed to study distant objects Large lenses are difficult and expensive to manufacture The weight of large lenses leads to sagging which produces aberrations
Reflecting Telescope n Helps overcome some of the disadvantages of refracting telescopes n n n Replaces the objective lens with a mirror The mirror is often parabolic to overcome spherical aberrations In addition, the light never passes through glass n n Except the eyepiece Reduced chromatic aberrations
Reflecting Telescope, Newtonian Focus n The incoming rays are reflected from the mirror and converge toward point A n n At A, a photographic plate or other detector could be placed A small flat mirror, M, reflects the light toward an opening in the side and passes into an eyepiece
Examples of Telescopes n Reflecting Telescopes n n n Largest in the world are 10 m diameter Keck telescopes on Mauna Kea in Hawaii Largest single mirror in US is 5 m diameter on Mount Palomar in California Refracting Telescopes n Largest in the world is Yerkes Observatory in Wisconsin n Has a 1 m diameter
Resolution n The ability of an optical system to distinguish between closely spaced objects is limited due to the wave nature of light If two sources of light are close together, they can be treated as noncoherent sources Because of diffraction, the images consist of bright central regions flanked by weaker bright and dark rings
Just Resolved n n If viewed through a slit of width a, and applying Rayleigh’s criterion, the limiting angle of resolution is For the images to be resolved, the angle subtended by the two sources at the slit must be greater than θmin
Barely Resolved (Left) and Not Resolved (Right)
Resolution with Circular Apertures n n The diffraction pattern of a circular aperture consists of a central, circular bright region surrounded by progressively fainter rings The limiting angle of resolution depends on the diameter, D, of the aperture
Diffraction Gratings
Diffraction Gratings 1
Diffraction Gratings 2
Diffraction Gratings 3
Diffraction Gratings 4
Michelson Interferometer n n The Michelson Interferometer is an optical instrument that has great scientific importance It splits a beam of light into two parts and then recombines them to form an interference pattern n It is used to make accurate length measurements
Michelson Interferometer, schematic n n A beam of light provided by a monochromatic source is split into two rays by a partially silvered mirror M One ray is reflected to M 1 and the other transmitted to M 2 After reflecting, the rays combine to form an interference pattern The glass plate ensures both rays travel the same distance through glass
Michelson Interferometer
Polarization Fig 38 -31, p. 1227
Polarization Application --Display
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