Chapter 34 Images One of the most important uses of the basic laws governing light is the production of images. Images are critical to a variety of fields and industries ranging from entertainment, security, and medicine In this chapter we define and classify images, and then classify several basic ways in which they can be produced. 34-1
Two Types of Images object lens real image object mirror virtual image Image: a reproduction derived from light Real Image: light rays actually pass through image, really exists in space (or on a screen for example) whether you are looking or not Virtual Image: no light rays actually pass through image. Only appear to be coming from image. Image only exists when rays are traced back to perceived 34-2 location of source
A Common Mirage Light travels faster through warm air warmer air has smaller index of refraction than colder air refraction of light near hot surfaces For observer in car, light appears to be coming from the road top ahead, but is really coming from sky. Fig. 34-1 34-3
Plane Mirrors, Point Object Plane mirror is a flat reflecting surface. Fig. 34-2 Identical triangles Ib = Ob Fig. 34-3 Plane Mirror: i = p Since I is a virtual image i < 0 34-4
Plane Mirrors, Extended Object Each point source of light in the extended object is mapped to a point in the image Fig. 34-4 Fig. 34-5 34-5
Plane Mirrors, Mirror Maze Your eye traces incoming rays straight back, and cannot know that the rays may have actually been reflected many times 1 2 8 3 9 7 6 4 5 4 2 3 1 6 5 8 7 9 Fig. 34-6 34-6
plane concave convex Fig. 34-7 Spherical Mirrors, Making a Spherical Mirror Plane mirror Concave Mirror 1. Center of Curvature C: in front at infinity in front but closer 2. Field of view wide smaller 3. Image i=p i >p 4. Image height image height = object height image height > object height Plane mirror Convex Mirror 1. Center of Curvature C: in front at infinity behind mirror and closer 2. Field of view wide larger 3. Image i=p i <p 4. Image height image height = object height image height < object height 34-7
Spherical Mirrors, Focal Points of Spherical Mirrors concave convex Fig. 34-8 Spherical Mirror: 1 2 r > 0 for concave (real focal point) r < 0 for convex (virtual focal point) f = r 34-8
Images from Spherical Mirrors Start with rays leaving a point on object, where they intersect, or appear to intersect marks the corresponding point on the image. Fig. 34-9 Real images form on the side where the object is located (side to which light is going). Virtual images form on the opposite side. Spherical Mirror: 1 1 1 + = Lateral Magnification: p i f Lateral Magnification: h ' m = h i m = p 34-9
Locating Images by Drawing Rays Fig. 34-10 1. A ray parallel to central axis reflects through F 2. A ray that reflects from mirror after passing through F, emerges parallel to central axis 3. A ray that reflects from mirror after passing through C, returns along itself 4. A ray that reflects from mirror after passing through c is reflected symmetrically about the central axis 34-10
Proof of the magnification equation Similar triangles (are angles same) Fig. 34-10 de cd de = cd = i, ca = p, = m ab ca ab i m = (magnification) p 34-11
Spherical Refracting Surfaces Fig. 34-11 Real images form on the side of a refracting surface that is opposite the object (side to which light is going). Virtual images form on the same side as the object. Spherical Refracting Surface: n n n n + = p i r 1 2 2 1 When object faces a convex refracting surface r is positive. When it faces a concave surface, r is negative. CAUTION: Reverse of of mirror sign convention! 34-12
Thin Lenses Converging lens Diverging lens Fig. 34-13 Thin Lens: 1 1 1 f p i 1 1 1 = f r1 r2 = + Thin Lens in air: ( n 1) Lens only can function if the index of the lens is different than that of its surrounding medium 34-13
Images from Thin Lenses Fig. 34-14 Real images form on the side of a lens that is opposite the object (side to which light is going). Virtual images form on the same side as the object. 34-14
Locating Images of Extended Objects by Drawing Rays Fig. 34-15 1. A ray initially parallel to central axis will pass through F 2 2. A ray that initially passes through F 1, will emerge parallel to central axis 3. A ray that initially is directed toward the center of the lens will emerge from the lens with no change in its direction (the two sides of the lens at the center are almost parallel) 34-15
Two Lens System O p 1 i 1 I 1 p 2 i 2 I 2 O 2 Lens 1 Lens 2 1. Let p 1 be the distance of object O from Lens 1. Use equation and/or principle rays to determine the distance to the image of Lens 1, i 1. 2. Ignore Lens 1, and use I 1 as the object O 2. If O 2 is located beyond Lens 2, then use a negative object distance p 1. Determine i 2 using the equation and/or principle rays to locate the final image I 2. The net magnification is: M = mm 1 2 34-16
Optical Instruments, Simple Magnifying Lens Can make an object appear larger (greater angular magnification) by simply bringing it closer to your eye. However, the eye cannot focus on objects closer that the near point p n ~25 cm BIG & BLURRY IMAGE A simple magnifying lens allows the object to be placed close by making a large virtual image that is far away. Simple Magnifier: m θ 25 cm f Fig. 34-17 Object at F 1 θ ' mθ = θ h θ = and θ ' 25 cm h f 34-17
Optical Instruments, Compound Microscope O close to F 1 I close to F 1 Mag. Lens Fig. 34-18 i s m= = since i s and p f p f M = mm = θ ob ob ey ob s 25 cm magnification compounded (microscope) f f 34-18
Optical Instruments, Refracting Telescope I close to F 2 and F 1 Mag. Lens Fig. 34-19 m ey θ = θob = θey θob fob fey m = θ θ f f ob ey h',, (telescope) h' 34-19
Fig. 34-20 Three Proofs, The Spherical Mirror Formula β = α + θ and γ = α + 2θ 1 θ = β α = ( γ α) α + γ = 2β 2 ac º ac º ac º ac º α =, β = = co p cc r ac º ac º γ = = CI i 1 f = r r = 2 f 2 ac º ac º ac º 1 1 1 + = 2 + = p i 2 f p i f 34-20
Three Proofs, The Refracting Surface Formula Fig. 34-21 n sinθ = n 1 1 2 2 1 1 2 2 1 2 1 2 ( α + β) = n ( β γ ) n + n = ( n n ) 1 2 sinθ nθ nθ if θ and θ are small θ = α + β and β = θ + γ n α γ β 1 2 2 1 ac º ac º ac º α ; β = ; γ p r i ac º ac º ac n ( ) º 1 + n2 = n2 n1 p i r n1 n2 n2 n + = p i r 1 34-21
Three Proofs, The Thin Lens Formulas Fig. 34-22 n n n n + = p i r 1 2 2 1 where n = 1 and n = n 1 2 1 n n 1 + = p' i' r' ( Eq. 34-22) p'' = i' + L n 1 1 n n 1 n 1 + = ; if L small + = ( Eq. 34-25 ) i' + L i'' r'' i' i'' r '' 1 1 1 1 1 1 1 1 ( Eq. 34-22 ) + ( Eq. 34-25) + = ( n 1) + = ( n 1) p' i'' r' r ' p i r' r '' 34-22