Copyright © 2009 Pearson Education, Inc. Chapter 33 Lenses and Optical Instruments

Copyright © 2009 Pearson Education, Inc. Basic parts of a camera: Lens Light-tight box Shutter Film or electronic sensor 33-5 Cameras: Film and Digital

Copyright © 2009 Pearson Education, Inc. 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 Cameras: Film and Digital

Copyright © 2009 Pearson Education, Inc Cameras: Film and Digital Example 33-8: Camera focus. How far must a 50.0-mm-focal- length camera lens be moved from its infinity setting to sharply focus an object 3.00 m away?

Copyright © 2009 Pearson Education, Inc. The human eye resembles a camera in its basic functioning, with an adjustable lens, the iris, and the retina The Human Eye; Corrective Lenses

Copyright © 2009 Pearson Education, Inc. Most of the refraction is done at the surface of the cornea; the lens makes small adjustments to focus at different distances The Human Eye; Corrective Lenses Figure goes here.

Copyright © 2009 Pearson Education, Inc. 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 The Human Eye; Corrective Lenses

Copyright © 2009 Pearson Education, Inc. Nearsightedness can be corrected with a diverging lens The Human Eye; Corrective Lenses

Copyright © 2009 Pearson Education, Inc. And farsightedness with a diverging lens The Human Eye; Corrective Lenses

Copyright © 2009 Pearson Education, Inc 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 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. 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 The Human Eye; Corrective Lenses

Copyright © 2009 Pearson Education, Inc. 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 Magnifying Glass

Copyright © 2009 Pearson Education, Inc. 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: 33-7 Magnifying Glass

Copyright © 2009 Pearson Education, Inc. 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 Aberrations of Lenses and Mirrors

Copyright © 2009 Pearson Education, Inc. Distortion: caused by variation in magnification with distance from the lens. Barrel and pincushion distortion: Aberrations of Lenses and Mirrors

Copyright © 2009 Pearson Education, Inc. Chromatic aberration: light of different wavelengths has different indices of refraction and focuses at different points Aberrations of Lenses and Mirrors

Copyright © 2009 Pearson Education, Inc. Solution: Achromatic doublet, made of lenses of two different materials Aberrations of Lenses and Mirrors

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. 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 Units of Chapter 34

Copyright © 2009 Pearson Education, Inc. 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 Waves versus Particles; Huygens’ Principle and Diffraction

Copyright © 2009 Pearson Education, Inc. Huygens’ principle is consistent with diffraction: 34-1 Waves versus Particles; Huygens’ Principle and Diffraction

Copyright © 2009 Pearson Education, Inc. 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 Huygens’ Principle and the Law of Refraction

Copyright © 2009 Pearson Education, Inc Huygens’ Principle and the Law of Refraction

Copyright © 2009 Pearson Education, Inc. The frequency of the light does not change, but the wavelength does as it travels into a new medium: 34-2 Huygens’ Principle and the Law of Refraction

Copyright © 2009 Pearson Education, Inc. Highway mirages are due to a gradually changing index of refraction in heated air Huygens’ Principle and the Law of Refraction

Copyright © 2009 Pearson Education, Inc. 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: 34-3 Interference – Young’s Double- Slit Experiment

Copyright © 2009 Pearson Education, Inc. If light is a wave, there should be an interference pattern Interference – Young’s Double- Slit Experiment

ConcepTest 34.1Superposition 1) 2) 3) 4) If waves A and B are superposed (that is, their amplitudes are added) the resultant wave is

The amplitudes of waves A and B have to be added at each point! ConcepTest 34.1Superposition 1) 2) 3) 4) If waves A and B are superposed (that is, their amplitudes are added) the resultant wave is

Copyright © 2009 Pearson Education, Inc. 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) Interference – Young’s Double- Slit Experiment

Copyright © 2009 Pearson Education, Inc. We can use geometry to find the conditions for constructive and destructive interference: 34-3 Interference – Young’s Double- Slit Experiment and

Copyright © 2009 Pearson Education, Inc. Between the maxima and the minima, the interference varies smoothly Interference – Young’s Double- Slit Experiment

Copyright © 2009 Pearson Education, Inc Interference – Young’s Double- Slit 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 Interference – Young’s Double- Slit Experiment Example 34-2: Line spacing for double-slit interference. A screen containing two slits 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 Interference – Young’s Double- Slit 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. Since the position of the maxima (except the central one) depends on wavelength, the first- and higher-order fringes contain a spectrum of colors Interference – Young’s Double- Slit Experiment

Copyright © 2009 Pearson Education, Inc 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 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 Intensity in the Double-Slit Interference Pattern The time-averaged intensity is proportional to the square of the field:

Copyright © 2009 Pearson Education, Inc Intensity in the Double-Slit Interference Pattern This plot shows the intensity as a function of angle.

Copyright © 2009 Pearson Education, Inc 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 I 0 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.

ConcepTest 34.3aDouble Slits I 1) spreads out 2) stays the same 3) shrinks together 4) disappears In a double-slit experiment, when the wavelength of the light is increased, the interference pattern

is increasedd does not change  must increase If is increased and d does not change, then  must increase, so the pattern spreads out. ConcepTest 34.3aDouble Slits I 1) spreads out 2) stays the same 3) shrinks together 4) disappears d sin  = m  d sin  = m  In a double-slit experiment, when the wavelength of the light is increased, the interference pattern

Copyright © 2009 Pearson Education, Inc. 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 Interference in Thin Films

Copyright © 2009 Pearson Education, Inc. 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 Interference in Thin Films

Copyright © 2009 Pearson Education, Inc. 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 Interference in Thin Films

Copyright © 2009 Pearson Education, Inc 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. Example 34-6: Thin film of air, wedge-shaped. A very fine wire 7.35 x 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? 34-5 Interference in Thin Films

Copyright © 2009 Pearson Education, Inc 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. 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 Interference in Thin Films

Copyright © 2009 Pearson Education, Inc Interference in Thin Films Example 34-8: Nonreflective coating. What is the thickness of an optical coating of MgF 2 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?

t 1) spaced farther apart 2) spaced closer together 3) no change ray 1 ray 2 ray 3 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? ConcepTest 34.6dParallel Slides IV

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 = m water water = air /n 2t = m water where water = air /n Thus, the water has decreased the wavelength of the light. t ray 1 ray 2 ray 3 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? ConcepTest 34.6dParallel Slides IV 1) spaced farther apart 2) spaced closer together 3) no change