Vern J Ostdiek Donald J Bord Chapter 9

Vern J. Ostdiek Donald J. Bord Chapter 9 Optics (Section 2)

9. 2 Mirrors: Plane and Not So Simple • Most mirrors that we use are plane mirrors: they are flat, smooth, almost perfect reflectors of light. • When we use a mirror to “see ourselves, ” light that is diffusely reflected off our clothes and face strikes the mirror and undergoes specular reflection.

9. 2 Mirrors: Plane and Not So Simple • Some of the rays leaving the mirror are going in the proper direction to enter our eyes and give us an image of ourselves. • The image appears to be on the other side of the mirror.

9. 2 Mirrors: Plane and Not So Simple • Instead of showing every light ray traveling outward from every point on the person, we show selected rays that happen to enter the person’s eyes. • The dashed lines from the image show the apparent paths taken by the rays when traced back to the image.

9. 2 Mirrors: Plane and Not So Simple • Applying the law of reflection and a little mathematics, it can be demonstrated that the image of an object in a plane mirror is as far behind the mirror’s surface as the object is in front of the mirror.

9. 2 Mirrors: Plane and Not So Simple • If you want to test this conclusion, point your index finger in the direction of a mirrored surface, and slowly move your hand toward the mirror. • The image of your finger will approach the mirror’s surface at the same rate that your real finger does and will arrive at the surface just as your finger touches it.

9. 2 Mirrors: Plane and Not So Simple • A number of important, practical devices employ plane mirrors. • They are used as optical levers to amplify small rotations in specialized laboratory instruments. • For example, as the mirror rotates through an angle q, the reflected beam will be turned through an angle 2 q.

9. 2 Mirrors: Plane and Not So Simple • A plane mirror is used in many reflex cameras to redirect light from the lens to the viewfinder. • When the shutter is pressed, the mirror tilts up, allowing the light to reach the film.

9. 2 Mirrors: Plane and Not So Simple • More recently, micromirrors, small enough to fit through the eye of needle (0. 5 mm or less), have become indispensable parts of modern telecommunications networks, where they are used in high-speed optical switches to control the flow of information through optical fibers.

9. 2 Mirrors: Plane and Not So Simple “One-Way Mirror” • A “one-way mirror” is made by partially coating glass so that it reflects some of the light and allows the rest to pass through. • This is called a half-silvered mirror.

9. 2 Mirrors: Plane and Not So Simple “One-Way Mirror” • When used as a window or wall between two rooms, it will function as a one-way mirror if one of the rooms is brightly lit and the other is dim. • It will appear to be an ordinary mirror to anyone in the bright room, but it will appear to be a window to anyone in the dim room. • This is because, in the bright room, the light reflected off the half-silvered mirror is much more intense than the light that passes through from the other room.

9. 2 Mirrors: Plane and Not So Simple “One-Way Mirror” • In the dim room, the transmitted light from the bright room dominates. • A person in the dim room can see what is happening in the bright room without being seen by anyone in the bright room.

9. 2 Mirrors: Plane and Not So Simple “One-Way Mirror” • This device is often used in interview and interrogation rooms and as a means of observing customers in stores and gambling casinos. windowpane. • Note that if a bright light is turned on in the dimmer room, the one-way effect is destroyed.

9. 2 Mirrors: Plane and Not So Simple “One-Way Mirror” • Ordinary window glass is a crude one-way mirror because it does reflect some of the light that strikes it. • At night, one can see into a brightly lit room through a window, but anyone in the room has difficulty seeing out because room light is reflected by the windowpane.

9. 2 Mirrors: Plane and Not So Simple Curved Mirrors • Reflectors—mirrors in this case—that are curved have useful properties. • Parallel light rays that reflect off a properly shaped concave mirror—a mirror that is curved inward—are focused at a point called the focal point.

9. 2 Mirrors: Plane and Not So Simple Curved Mirrors • The energy in the light is concentrated at that point. • Sunlight focused by a concave mirror can heat things to very high temperatures.

9. 2 Mirrors: Plane and Not So Simple Curved Mirrors • Even when a mirror’s surface is curved, the law of reflection still holds at each point that a ray strikes the mirror. • If a normal line is drawn at each point (as was done in the figure below), the angle of incidence equals the angle of reflection.

9. 2 Mirrors: Plane and Not So Simple Curved Mirrors • One such normal line is shown in the figure. • A concave mirror can be used to form images that are enlarged—magnified. • Magnifying makeup and shaving mirrors are concave mirrors, as are the large mirrors used in astronomical telescopes.

9. 2 Mirrors: Plane and Not So Simple Curved Mirrors • The figure shows a magnified image seen in a concave mirror.

9. 2 Mirrors: Plane and Not So Simple Curved Mirrors • A convex mirror is one that is curved outward. • The image formed by a convex mirror is reduced—it is smaller than the image formed by a plane mirror.

9. 2 Mirrors: Plane and Not So Simple Curved Mirrors • The advantage of a convex mirror is that it has a wide field of view—images of things spread over a wide area can be viewed in it. • The figure shows the fields of view for a convex mirror and a plane mirror of the same size.

9. 2 Mirrors: Plane and Not So Simple Curved Mirrors • One glance at a well- placed convex mirror on a bike path allows quick surveillance of a large area.

9. 2 Mirrors: Plane and Not So Simple Curved Mirrors • Passenger-side rearview mirrors on cars and auxiliary “wide-angle” rearview mirrors on trucks and other vehicles are convex so the driver can view a large region to the rear. • Care must be taken when using such a mirror because the reduced image makes any object appear to be farther away than it actually is.

9. 2 Mirrors: Plane and Not So Simple Astronomical Telescope Mirrors • The largest telescopes used by astronomers to examine stars, galaxies, and other celestial objects make use of curved mirrors. • The figure shows a common design for such telescopes.

9. 2 Mirrors: Plane and Not So Simple Astronomical Telescope Mirrors • Light from the distant source enters the telescope and reflects off a large concave mirror called the primary mirror. • • The reflected rays converge onto a much smaller convex mirror called the secondary mirror. The rays are reflected back toward the primary mirror, pass through a hole in its center, and converge to form an image at the focal point F. • The primary mirror is the key component of the telescope.

9. 2 Mirrors: Plane and Not So Simple Astronomical Telescope Mirrors • Telescope mirrors have as their basic functions the gathering of light and the concentration of that light to a point. • • The ability of a mirror to collect light increases with its surface area. To acquire enough radiation to study faint objects adequately, astronomers have sought to build instruments with larger and larger apertures (openings) and, hence, larger light-collecting areas.

9. 2 Mirrors: Plane and Not So Simple Astronomical Telescope Mirrors • The quality of the images produced by telescopes is greatly affected by the shapes of the mirrors. • The easiest curved mirror to make is one that has a surface that has the shape of part of a sphere. • But such a spherical mirror is not perfect for the task of focusing light rays.

9. 2 Mirrors: Plane and Not So Simple Astronomical Telescope Mirrors • The figure shows that parallel light rays reflecting off a spherical mirror are not all focused at the same point. • An image formed using such a mirror will be somewhat blurred. • This phenomenon is called spherical aberration. • As the name implies, spherical aberration is a defect associated with spherical surfaces.

9. 2 Mirrors: Plane and Not So Simple Astronomical Telescope Mirrors • A concave mirror in the shape of a parabola does not have this aberration. • A parabolic mirror will concentrate all the rays coming from a distant source at the same point.

9. 2 Mirrors: Plane and Not So Simple Astronomical Telescope Mirrors • Thus, the ideal surface for a telescope mirror (or for that matter, reflectors in auto headlamps and household flashlights) is one shaped like a parabola. • • Fabricating very large mirrors, some as big as 10 meters (33 feet) in diameter, with the precise parabolic shape is an enormous technical challenge. One technique called spin casting exploits the fact that the surface of a liquid rotating at a steady rate has the required parabolic shape.

9. 2 Mirrors: Plane and Not So Simple Astronomical Telescope Mirrors • Since the 1980 s, several telescopes have been constructed that employ rotating liquid mirrors, the most ambitious being the 6 -meter Large Zenith Telescope (LZT) in British Columbia. • In the simplest designs, a large bowl of mercury is spun at the proper rate to produce a surface with the desired parabolic shape.

9. 2 Mirrors: Plane and Not So Simple Astronomical Telescope Mirrors • Although such liquid mirror telescopes can’t be tilted and can only examine the sky nearly directly above them, they are relatively cheap to build: • The 6 -meter LZT cost only about $1 million, 100 times less than a comparable conventional glass mirror telescope.

9. 2 Mirrors: Plane and Not So Simple Astronomical Telescope Mirrors • Shortly after the Hubble Space Telescope (HST) was placed in orbit on 25 April 1990, scientists discovered that its primary mirror was afflicted with a type of spherical aberration.

9. 2 Mirrors: Plane and Not So Simple Astronomical Telescope Mirrors • At the edge of the 2. 4 -meter-diameter mirror, its surface is misshapen by 0. 002 millimeters from what it is supposed to be. • This seemingly minuscule error drastically reduced the telescope’s ability to form sharp images. • In December 1993, space shuttle astronauts installed corrective optics on the instrument platform of the Space Telescope to alleviate this problem and allow the observatory to perform as designed.

9. 2 Mirrors: Plane and Not So Simple Astronomical Telescope Mirrors • The figure shows the dramatic improvement in the ability of the Space Telescope to resolve fine detail as a result of the repairs.

9. 2 Mirrors: Plane and Not So Simple Astronomical Telescope Mirrors • Further improvements in the performance of HST have occurred with the installation of the Advanced Camera for Surveys (ACS) in the spring of 2002. • The ACS replaced an earlier camera and, with its higher resolution, larger field of view, and greater light collection efficiency, has provided about a factor-of-ten improvement in the capability of the Space Telescope.

9. 2 Mirrors: Plane and Not So Simple Astronomical Telescope Mirrors • From the ground, recent efforts to combat the blurring effects of Earth’s atmosphere and thereby to increase the resolution of optical instruments, have involved the use of “adaptive optics” (AO). • Here, elaborate wavefront sensors, fast computers, and deformable mirrors are used to produce images so sharp that it’s as though the atmosphere had disappeared entirely.

9. 2 Mirrors: Plane and Not So Simple Astronomical Telescope Mirrors • The figure shows a typical design of an AO system, similar to those in use with the two 10 -m Keck Telescopes in Hawaii, the 8. 2 -m Gemini North (Hawaii) and South (Chile) instruments, and the Very Large Telescope array (Chile).

9. 2 Mirrors: Plane and Not So Simple Astronomical Telescope Mirrors • The key optical element is the “rubber mirror”—a thin glass mirror that has a surface that can be slightly deformed by up to a hundred tiny actuators attached to the back.

9. 2 Mirrors: Plane and Not So Simple Curved Mirrors • If the tiny deformations in the rubber mirror can be made to counteract the deformations in the wavefronts from distant sources caused by turbulence in Earth’s atmosphere, then the original wavefronts can be restored and the blurring in the image removed. • Fast computers are required to monitor continuously the rapidly changing conditions in the atmosphere, compute the necessary corrections, and signal the accuators to move appropriately.

9. 2 Mirrors: Plane and Not So Simple Curved Mirrors • This technique normally uses a bright star in the field of view of the telescope as the reference beacon for the wavefront assessment. • In the absence of such a star, an artificial one can be created using a high-power, highly focused laser beam projected up through the telescope.

9. 2 Mirrors: Plane and Not So Simple Curved Mirrors • Called “laser guidestars, ” the light from the beam that is scattered downward either from air molecules at altitudes of 10 to 40 km or from sodium atoms residing as high as 90 km produces a faint but measurable target for the wavefront sensors.

9. 2 Mirrors: Plane and Not So Simple Curved Mirrors • As indispensable as AO systems are for optimizing the light-gathering and resolving power of large, 10 -m class telescopes, still greater advances will be needed in this field to harness the full capabilities of the really large telescopes with 20 -m apertures or larger planned for the future. • To meet the challenges, new initiatives described as “atmospheric tomography”—similar to “medical tomography” where a 3 -D view of a patient is produced—will be required.

Concept Map 9. 1