Ch 19 Accommodation Accommodation is the adjustment of lens shape to focus the image onto the retina. Muscles pull on lens and change its shape. Near Point ( N ) closest distance that the eye can focus clearly. For “normal” eye, near point 25 cm. Far Point: farthest point that eye can focus. For “normal” eye, far point is infinity (i.e. parallel rays). Nearsightedness: eye that can focus only on nearby objects. Farsightedness: eye that cannot focus on nearby objects Relaxed Eye: focused on infinity Astigmatism: Out of round cornea or lens. Ch 19 Correcting Eye Defects with Lenses Ch 19 Rayleigh Criterion Resolution: ability of a lens to produce distinct images of two point objects Resolution is limited by Various aberrations Diffraction Rayleigh Criterion: angular limit of resolution of light of wavelength passing through a lens of diameter D. The factor of 1.22 results from treating a circular hole as the average of a slit. Ch 19 Example 25-4: A spy satellite carries out surveillance with a special high-resolution camera with a lens diameter of 40.0 cm that is limited only by diffraction. Estimate the separation of two small objects on the surface of the earth that can be resolved in the light of 500 nm if the satellite is 250 km above the surface of the earth. θ r s Ch 19 Astronomical Refracting Telescope The telescope shown above produces an inverted image Objective lens forms real image at its focal point (fo) Eyepiece ( fe ) acts as a magnifying glass on this image Θ h / fo where h is image from objective and tanθ θ θ’ h / fe (look at thick ray which is parallel to axis) The magnification is: M = θ’ / θ and thus: Negative M indicates an inverted image. Ch 19 Chapter 26 Relativity Giancoli, PHYSICS,6/E © 2005. Electronically reproduced by permission of Pearson Education, Inc., Upper Saddle River, New Jersey Ch 19 Galilian-Newtonian Relativity Relativity deals with experiments observed from different reference frames. Example: Person drops coin from moving car In reference frame of car: coin is at rest and falls straight down In “earth” reference frame, coin is moving with initial velocity and follows projectile path. Ch 19 Inertial Reference Frames Inertial Reference Frame: one in which Newton’s First Law (Law of Inertia is valid.) A reference frame moving with constant velocity with respect to an inertial reference frame is an inertial frame. If the car is moving with constant velocity relative to the earth, it is an inertial reference frame. Accelerated or rotating reference frames are noninertial reference frames. The earth is approximately inertial. Ch 19 Early Relativity Principle “the basic laws of physics are the same in all inertial reference frames” This principle was understood by Galileo and Newton. Space and time are absolute– different inertial reference frames measure the same length, time etc. All inertial reference frames are equivalent– there is no preferred frame. Ch 19 Special Theory of Relativity Einstein asked the question “What would happen if I rode a light beam?” Would see static electric and magnetic fields with no understandable source. Understanding electromagnetic radiation requires changing E and B fields. Concluded that: no one could travel at speed of light. No one could be in frame where speed of light was anything other than c. No absolute reference frame Ch 19 Postulates of Special Theory of Relativity First: The laws of physics have the same form in all inertial reference frames Second: Light propagates through empty space with a definite speed c independent of the source and observer This means that an observer trying to catch a light beam and moving at 0.9c will measure the speed of that light as c and an observer on earth will also measure c. In order for this to be true, observers must differ on measurements of distance and time The special theory of relativity deals with reference frames that move at constant velocity with respect to an inertial reference frame. The General Theory deals with accelerated reference frames and is primarily a theory of gravity. Ch 19 Relativistic Clock In the above clock, light is reflected back and forth between two mirrors and timer counts “ticks” This is an ideal clock because of special properties of light An observer at rest with respect to the clock concludes that the time for a tick is In order to study time dilation, we will places this clock in a spaceship moving past earth. t0 is called proper or rest time because clock is at rest in spaceship (note, we don’t call it “correct” time) Ch 19 Time dilation Spaceship moves by earth at speed v. (both observers agree that speed is v.) Observer on earth sees light move distance per tick. Observer on earth sees spaceship moving Observer on earth sees the time in the space ship. Ch 19 Substituting for L Substituting Ch 19 Time dilation Clocks moving relative to an observer are measured by that observer to run more slowly (as compared to clocks at rest). Clock is in spaceship so this measures the proper or rest time Δt0. It is often convenient to write v as fraction of c, thus v = 3.0x107 m/s is written v = 0.10 c. We call this effect time dilation because the time in the moving reference frame is always longer than the time in the proper reference frame Ch 19 Time dilation factor Consider how this depends on v v (m/s) v (c) t0 (sec) t (sec) 2.00x105 0.00067 c 1.00000 1.00000 3.00x106 0.01000c 1.00000 1.00005 3.00x107 0.10000c 1.00000 1.00500 2.00x108 0.66667c 1.00000 1.34200 2.97x108 0.99000c 1.00000 7.08900