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Chapter 33 Lenses and Optical Instruments Copyright © 2009 Pearson Education, Inc. 33-5 Cameras: Film and Digital Basic parts of a camera: • Lens • Light-tight box • Shutter • Film or electronic sensor Copyright © 2009 Pearson Education, Inc. 33-5 Cameras: Film and Digital Camera adjustments: • Shutter speed: controls the amount of time light enters the camera. A faster shutter speed makes a sharper picture. • f-stop: controls the maximum opening of the shutter. This allows the right amount of light to enter to properly expose the film, and must be adjusted for external light conditions. • Focusing: this adjusts the position of the lens so that the image is positioned on the film. Copyright © 2009 Pearson Education, Inc. 33-5 Cameras: Film and Digital Example 33-8: Camera focus. How far must a 50.0-mm-focallength camera lens be moved from its infinity setting to sharply focus an object 3.00 m away? Copyright © 2009 Pearson Education, Inc. 33-6 The Human Eye; Corrective Lenses The human eye resembles a camera in its basic functioning, with an adjustable lens, the iris, and the retina. Copyright © 2009 Pearson Education, Inc. 33-6 The Human Eye; Corrective Lenses Figure 33-26 goes here. Most of the refraction is done at the surface of the cornea; the lens makes small adjustments to focus at different distances. Copyright © 2009 Pearson Education, Inc. 33-6 The Human Eye; Corrective Lenses Near point: closest distance at which eye can focus clearly. Normal is about 25 cm. Far point: farthest distance at which object can be seen clearly. Normal is at infinity. Nearsightedness: far point is too close. Farsightedness: near point is too far away. Copyright © 2009 Pearson Education, Inc. 33-6 The Human Eye; Corrective Lenses Nearsightedness can be corrected with a diverging lens. Copyright © 2009 Pearson Education, Inc. 33-6 The Human Eye; Corrective Lenses And farsightedness with a diverging lens. Copyright © 2009 Pearson Education, Inc. 33-6 The Human Eye; Corrective Lenses Example 33-12: Farsighted eye. Sue is farsighted with a near point of 100 cm. Reading glasses must have what lens power so that she can read a newspaper at a distance of 25 cm? Assume the lens is very close to the eye. Copyright © 2009 Pearson Education, Inc. 33-6 The Human Eye; Corrective Lenses Example 33-13: Nearsighted eye. A nearsighted eye has near and far points of 12 cm and 17 cm, respectively. (a) What lens power is needed for this person to see distant objects clearly, and (b) what then will be the near point? Assume that the lens is 2.0 cm from the eye (typical for eyeglasses). Copyright © 2009 Pearson Education, Inc. 33-6 The Human Eye; Corrective Lenses Vision is blurry under water because light rays are bent much less than they would be if entering the eye from air. This can be avoided by wearing goggles. Copyright © 2009 Pearson Education, Inc. 33-7 Magnifying Glass A magnifying glass (simple magnifier) is a converging lens. It allows us to focus on objects closer than the near point, so that they make a larger, and therefore clearer, image on the retina. Copyright © 2009 Pearson Education, Inc. 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: Copyright © 2009 Pearson Education, Inc. 33-10 Aberrations of Lenses and Mirrors Spherical aberration: rays far from the lens axis do not focus at the focal point. Solutions: compound-lens systems; use only central part of lens. Copyright © 2009 Pearson Education, Inc. 33-10 Aberrations of Lenses and Mirrors Distortion: caused by variation in magnification with distance from the lens. Barrel and pincushion distortion: Copyright © 2009 Pearson Education, Inc. 33-10 Aberrations of Lenses and Mirrors Chromatic aberration: light of different wavelengths has different indices of refraction and focuses at different points. Copyright © 2009 Pearson Education, Inc. 33-10 Aberrations of Lenses and Mirrors Solution: Achromatic doublet, made of lenses of two different materials Copyright © 2009 Pearson Education, Inc. Summary of Chapter 33 • Lens uses refraction to form real or virtual image. • Converging lens: rays converge at focal point. • Diverging lens: rays appear to diverge from focal point. • Power is given in diopters (m-1): Copyright © 2009 Pearson Education, Inc. Summary of Chapter 33 • Thin lens equation: • Magnification: Copyright © 2009 Pearson Education, Inc. Summary of Chapter 33 • Camera focuses image on film or electronic sensor; lens can be moved and size of opening adjusted (f-stop). • Human eye also makes adjustments, by changing shape of lens and size of pupil. • Nearsighted eye is corrected by diverging lens. • Farsighted eye is corrected by converging lens. Copyright © 2009 Pearson Education, Inc. Summary of Chapter 33 • Magnification of simple magnifier: • Telescope: objective lens or mirror plus eyepiece lens. Magnification: Copyright © 2009 Pearson Education, Inc. Chapter 34 The Wave Nature of Light; Interference Copyright © 2009 Pearson Education, Inc. Units of Chapter 34 • Waves versus Particles; Huygens’ Principle and Diffraction • Huygens’ Principle and the Law of Refraction • Interference – Young’s Double-Slit Experiment • Intensity in the Double-Slit Interference Pattern • Interference in Thin Films • Michelson Interferometer • Luminous Intensity Copyright © 2009 Pearson Education, Inc. 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. Copyright © 2009 Pearson Education, Inc. 34-1 Waves versus Particles; Huygens’ Principle and Diffraction Huygens’ principle is consistent with diffraction: Copyright © 2009 Pearson Education, Inc. D 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. Copyright © 2009 Pearson Education, Inc. 34-2 Huygens’ Principle and the Law of Refraction Copyright © 2009 Pearson Education, Inc. 34-2 Huygens’ Principle and the Law of Refraction The frequency of the light does not change, but the wavelength does as it travels into a new medium: Copyright © 2009 Pearson Education, Inc. 34-2 Huygens’ Principle and the Law of Refraction Highway mirages are due to a gradually changing index of refraction in heated air. Copyright © 2009 Pearson Education, Inc. 34-3 Interference – Young’s DoubleSlit Experiment If light is a wave, interference effects will be seen, where one part of a wave front can interact with another part. One way to study this is to do a double-slit experiment: Copyright © 2009 Pearson Education, Inc. 34-3 Interference – Young’s DoubleSlit Experiment If light is a wave, there should be an interference pattern. Copyright © 2009 Pearson Education, Inc. ConcepTest 34.1 Superposition If waves A and B are superposed (that is, their amplitudes are added) the resultant wave is 1) 2) 3) 4) ConcepTest 34.1 Superposition If waves A and B are superposed (that is, their amplitudes are added) the resultant wave is 1) The amplitudes of waves A and B have to 2) be added at each point! 3) 4) 34-3 Interference – Young’s DoubleSlit 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). Copyright © 2009 Pearson Education, Inc. 34-3 Interference – Young’s DoubleSlit Experiment We can use geometry to find the conditions for constructive and destructive interference: and Copyright © 2009 Pearson Education, Inc. 34-3 Interference – Young’s DoubleSlit Experiment Between the maxima and the minima, the interference varies smoothly. Copyright © 2009 Pearson Education, Inc. D 34-3 Interference – Young’s DoubleSlit Experiment Conceptual Example 34-1: Interference pattern lines. (a) Will there be an infinite number of points on the viewing screen where constructive and destructive interference occur, or only a finite number of points? (b) Are neighboring points of constructive interference uniformly spaced, or is the spacing between neighboring points of constructive interference not uniform? Copyright © 2009 Pearson Education, Inc. 34-3 Interference – Young’s DoubleSlit Experiment Example 34-2: Line spacing for double-slit interference. A screen containing two slits 0.100 mm apart is 1.20 m from the viewing screen. Light of wavelength λ = 500 nm falls on the slits from a distant source. Approximately how far apart will adjacent bright interference fringes be on the screen? Copyright © 2009 Pearson Education, Inc. 34-3 Interference – Young’s DoubleSlit Experiment Conceptual Example 34-3: Changing the wavelength. (a) What happens to the interference pattern in the previous example if the incident light (500 nm) is replaced by light of wavelength 700 nm? (b) What happens instead if the wavelength stays at 500 nm but the slits are moved farther apart? Copyright © 2009 Pearson Education, Inc. 34-3 Interference – Young’s DoubleSlit Experiment Since the position of the maxima (except the central one) depends on wavelength, the firstand higher-order fringes contain a spectrum of colors. Copyright © 2009 Pearson Education, Inc. 34-4 Intensity in the Double-Slit Interference Pattern The electric fields at the point P from the two slits are given by . where Copyright © 2009 Pearson Education, Inc. 34-4 Intensity in the Double-Slit Interference Pattern The two waves can be added using phasors, to take the phase difference into account: Copyright © 2009 Pearson Education, Inc. 34-4 Intensity in the Double-Slit Interference Pattern The time-averaged intensity is proportional to the square of the field: Copyright © 2009 Pearson Education, Inc. 34-4 Intensity in the Double-Slit Interference Pattern This plot shows the intensity as a function of angle. Copyright © 2009 Pearson Education, Inc. 34-4 Intensity in the Double-Slit Interference Pattern Example 34-5: Antenna intensity. Two radio antennas are located close to each other, separated by a distance d. The antennas radiate in phase with each other, emitting waves of intensity I0 at wavelength λ. (a) Calculate the net intensity as a function of θ for points very far from the antennas. (b) For d = λ, determine I and find in which directions I is a maximum and a minimum. (c) Repeat part (b) when d = λ/2. Copyright © 2009 Pearson Education, Inc. ConcepTest 34.3a Double Slits I In a double-slit experiment, 1) spreads out when the wavelength of the light 2) stays the same is increased, the interference 3) shrinks together pattern 4) disappears ConcepTest 34.3a Double Slits I In a double-slit experiment, 1) spreads out when the wavelength of the light 2) stays the same is increased, the interference 3) shrinks together pattern d sin = m If is increased and d does not change, then must increase, so the pattern spreads out. 4) disappears 34-5 Interference in Thin Films Another way path lengths can differ, and waves interfere, is if they travel through different media. If there is a very thin film of material – a few wavelengths thick – light will reflect from both the bottom and the top of the layer, causing interference. This can be seen in soap bubbles and oil slicks. Copyright © 2009 Pearson Education, Inc. D 34-5 Interference in Thin Films The wavelength of the light will be different in the oil and the air, and the reflections at points A and B may or may not involve phase changes. Copyright © 2009 Pearson Education, Inc. 34-5 Interference in Thin Films A similar effect takes place when a shallowly curved piece of glass is placed on a flat one. When viewed from above, concentric circles appear that are called Newton’s rings. Copyright © 2009 Pearson Education, Inc. 34-5 Interference in Thin Films A beam of light reflected by a material with index of refraction greater than that of the material in which it is traveling, changes phase by 180° or ½ cycle. Copyright © 2009 Pearson Education, Inc. 34-5 Interference in Thin Films Example 34-6: Thin film of air, wedge-shaped. A very fine wire 7.35 x 10-3 mm in diameter is placed between two flat glass plates. Light whose wavelength in air is 600 nm falls (and is viewed) perpendicular to the plates and a series of bright and dark bands is seen. How many light and dark bands will there be in this case? Will the area next to the wire be bright or dark? Copyright © 2009 Pearson Education, Inc. 34-5 Interference in Thin Films Example 34-7: Thickness of soap bubble skin. A soap bubble appears green (λ = 540 nm) at the point on its front surface nearest the viewer. What is the smallest thickness the soap bubble film could have? Assume n = 1.35. Copyright © 2009 Pearson Education, Inc. 34-5 Interference in Thin Films Problem Solving: Interference 1. Interference occurs when two or more waves arrive simultaneously at the same point in space. 2. Constructive interference occurs when the waves are in phase. 3. Destructive interference occurs when the waves are out of phase. 4. An extra half-wavelength shift occurs when light reflects from a medium with higher refractive index. Copyright © 2009 Pearson Education, Inc. 34-5 Interference in Thin Films Example 34-8: Nonreflective coating. What is the thickness of an optical coating of MgF2 whose index of refraction is n = 1.38 and which is designed to eliminate reflected light at wavelengths (in air) around 550 nm when incident normally on glass for which n = 1.50? Copyright © 2009 Pearson Education, Inc. ConcepTest 34.6d Two identical microscope slides in air illuminated with light from a laser are creating an interference pattern. The space between the slides is now filled with water (n = 1.33). What happens to the interference fringes? Parallel Slides IV 1) spaced farther apart 2) spaced closer together 3) no change ray 1 ray 2 ray 3 t ConcepTest 34.6d Two identical microscope slides in air illuminated with light from a laser are creating an interference pattern. The space between the slides is now filled with water (n=1.33). What happens to the interference fringes? Parallel Slides IV 1) spaced farther apart 2) spaced closer together 3) no change The path difference between ray 2 and ray 3 is 2t (in addition, ray 3 experiences a phase change of 180°). Thus, the dark fringes will occur for: 2t = mwater where water = air/n Thus, the water has decreased the wavelength of the light. ray 1 ray 2 ray 3 t