1 Optics Electromagnetic spectrum polarization Laws of reflection and refraction TIR –Images –Mirrors and lenses –Real/virtual, inverted/straight, bigger/smaller

2 hitt The Sun is about 1.5 X m away. The time for light to travel this distance is about: A. 4.5 x s B. 8 s C. 8 min D. 8 hr E. 8 yr

3 The index of refraction n encountered by light in any medium except vacuum depends on the wavelength of the light. So if light consisting of different wavelengths enters a material, the different wavelengths will be refracted differently  chromatic dispersion Chromatic Dispersion 33- Fig Fig n 2blue >n 2red Chromatic dispersion can be good (e.g., used to analyze wavelength composition of light) or bad (e.g., chromatic aberration in lenses)

4 Chromatic Dispersion 33- Fig Chromatic dispersion can be good (e.g., used to analyze wavelength composition of light) or bad (e.g., chromatic aberration in lenses) prism lens

5 Rainbows 33- Fig Sunlight consists of all visible colors and water is dispersive, so when sunlight is refracted as it enters water droplets, is reflected off the back surface, and again is refracted as it exits the water drops, the range of angles for the exiting ray will depend on the color of the ray. Since blue is refracted more strongly than red, only droplets that are closer the the rainbow center ( A ) will refract/reflect blue light to the observer ( O ). Droplets at larger angles will still refract/reflect red light to the observer. What happens for rays that reflect twice off the back surfaces of the droplets?

6 For light that travels from a medium with a larger index of refraction to a medium with a smaller medium of refraction n 1 >n 1   2 >  1, as  1 increases,  2 will reach 90 o (the largest possible angle for refraction) before  1 does. Total Internal Reflection 33- Fig n1n1 n2n2 Critical Angle: When  2 >  c no light is refracted (Snell’s Law does not have a solution!) so no light is transmitted  Total Internal Reflection Total internal reflection can be used, for example, to guide/contain light along an optical fiber

7 Polarization by Reflection 33- Fig Brewster’s Law Applications 1.Perfect window: since parallel polarization is not reflected, all of it is transmitted 2.Polarizer: only the perpendicular component is reflected, so one can select only this component of the incident polarization Brewster Angle: In which direction does light reflecting off a lake tend to be polarized? When the refracted ray is perpendicular to the reflected ray, the electric field parallel to the page (plane of incidence) in the medium does not produce a reflected ray since there is no component of that field perpendicular to the reflected ray (EM waves are transverse).

8 Chapter 34 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. Images 34-

9 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 location of source Two Types of Images 34- object lens real image object mirror virtual image

10 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. A Common Mirage 34- Fig. 34-1

11 Plane mirror is a flat reflecting surface. Plane Mirrors, Point Object 34- Fig Fig Identical triangles Plane Mirror: Since I is a virtual image i < 0

12 Each point source of light in the extended object is mapped to a point in the image Plane Mirrors, Extended Object 34- Fig Fig. 34-5

13 Your eye traces incoming rays straight back, and cannot know that the rays may have actually been reflected many times Plane Mirrors, Mirror Maze 34- Fig

14 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 34- Fig 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 Spherical Mirrors, Making a Spherical Mirror concave plane convex

15 Spherical Mirrors, Focal Points of Spherical Mirrors 34- Fig concave convex Spherical Mirror: r > 0 for concave (real focal point) r < 0 for convex (virtual focal point)

16 Start with rays leaving a point on object, where they intersect, or appear to intersect marks the corresponding point on the image. Images from Spherical Mirrors 34- Fig 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: Lateral Magnification:

17 Locating Images by Drawing Rays 34- Fig 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

18 Proof of the magnification equation 34- Fig Similar triangles (are angles same)

19 Spherical Refracting Surfaces 34- Fig 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: 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!

Fig Converging lens Diverging lens Thin Lens: Thin Lens in air: Lens only can function if the index of the lens is different than that of its surrounding medium Thin Lenses

21 Images from Thin Lenses 34- Fig 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.

22 Locating Images of Extended Objects by Drawing Rays 34- Fig 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)

23 Two Lens System 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. Lens 1 Lens 2 p1p1 O I1I1 i1i1 O2O2 p2p2 I2I2 i2i2

24 Optical Instruments, Simple Magnifying Lens 34- Fig 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: Object at F 1

Fig Optical Instruments, Compound Microscope I close to F 1 ’ O close to F 1 Mag. Lens

26 Optical Instruments, Refracting Telescope 34- Fig I close to F 2 and F 1 ’ Mag. Lens

27 Three Proofs, The Spherical Mirror Formula 34- Fig

28 Three Proofs, The Refracting Surface Formula 34- Fig

Fig Three Proofs, The Thin Lens Formulas

30 hitt A point source emits electromagnetic energy at a rate of 100W. The intensity 10 m from the source is: A. 10 W/m 2 B. 1.6 W/m 2 C. 1 W/m 2 D. 0:024 W/m 2 E. 0:080 W/m 2