Physics 1202: Lecture 18 Today s Agenda Announcements: Team problems today Team 10: Alisha Kumar, Adam Saxton, Alanna Forsberg Team 11: Riley Burns, Deanne Edwards, Shauna Bolton Team 12: Kervell Baird, Matthew George, Derek Schultz Homework #8: due Friday Midterm 2: Tuesday April 10: covers Ch. 23-27. Office hours if needed (M-2:30-3:30 or TH 3:00-4:00) Chapter 26: Review of Refraction Total internal reflection Refraction and polarization Equation for lenses Dispersion & rainbows h o f i h 1
EM wave at an interface What happens when light hits a surface of a material? Three Possibilities Reflected Refracted (transmitted) Absorbed Snell s Law incident ray q 1 q r reflected ray MATERIAL 1: n 1 q 2 refracted ray MATERIAL 2: n 2 26-5 Refraction: Basic properties Light may refract into a material where its speed is lower angle of refraction is less than the angle of incidence The ray bends toward the normal Light may refract into a material where its speed is higher angle of refraction is more than the angle of incidence The ray bends away from the normal If n 1 = n 2 Þ no effect If light enters normal Þ no effect 2
Lecture 18, ACT 1 Which of the following ray diagrams could represent the passage of light from air through glass and back to air? (a) (b) (c) Optical effect Refraction can make objects immersed in water appear broken Refraction can create mirages 3
Lecture 18, ACT 2 Which of the following ray diagrams could represent the passage of light from air through glass and back to air? (a) (b) (c) (d) Total Internal Reflection Consider light moving from glass (n 1 =1.5) to air (n 2 =1.0) n 1 n 2 incident ray q 1 q r q 2 refracted ray reflected ray GLASS AIR ie light is bent away from the normal. as q 1 gets bigger, q 2 gets bigger, but q 2 can never get bigger than 90!! In general, if sin q 1 ³ sin q C ³ (n 2 / n 1 ), we have NO refracted ray; we have TOTAL INTERNAL REFLECTION. For example, light in water which is incident on an air surface with angle q 1 > q c = sin -1 (1.0/1.5) = 41.8 will be totally reflected. This property is the basis for the optical fibers used in communication. 4
An optical fiber is cladded by another dielectric. In case I this is water, with an index of refraction of 1.33, while in case II this is air with an index of refraction of 1.00. ACT 3: Critical Angle... Compare the critical angles for total internal reflection in these two cases a) q ci >q cii b) q ci =q cii c) q ci <q cii Case I Case II q c q c water n =1.33 glass n =1.5 water n =1.33 air n =1.00 glass n =1.5 air n =1.00 The same two fibers are used to transmit light from a laser in one room to an experiment in another. Which makes a better fiber, the one in water (I) or the one in air (II)? a) I Water b) II Air ACT 4: Fiber Optics Case I Case II q c q c water n =1.33 glass n =1.5 water n =1.33 air n =1.00 glass n =1.5 air n =1.00 5
26-5 Applications of TIR Total internal reflection (TIR) is used in some binoculars in optical fibers In other optical devices 2017 Pearson Education, Inc. Internal Reflection in a Prism Submarine Periscopes to see around corners 6
An application of internal reflection Plastic or glass rods are used to pipe light from one place to another Fiber Optics Applications include medical use of fiber optic cables for diagnosis and correction of medical problems Telecommunications 26-5 Refraction & polarization Brewster s angle special angle light reflected is totally polarized Reflected light is completely polarized When angle between reflected and refracted beams is 90 o Polarization is parallel to the reflecting surface Applications Remove reflection Photographs of objects in water 7
26-5 Applications of TIR Total internal reflection (TIR) is used in some binoculars in optical fibers In other optical devices 2017 Pearson Education, Inc. h R-i R q q & o-r o h i h o f i h 8
Mirror Lens Definitions Some important terminology we introduced last class, o = distance from object to mirror (or lens) i = distance from mirror to image o positive, i positive if on same side of mirror as o. R = radius of curvature of spherical mirror f = focal length, = R/2 for spherical mirrors. Concave, Convex, and Spherical mirrors. M = magnification, (size of image) / (size of object) negative means inverted image R a a h object q b g image i o 26-6 Ray Tracing for Lenses A lens is a piece of transparent material shaped such that parallel light rays are refracted towards a point, a focus: Convergent Lens» light moving from air into glass will move toward the normal» light moving from glass back into air will move away from the normal» real focus Divergent Lens» light moving from air into glass will move toward the normal» light moving from glass back into air will move away from the normal» virtual focus 9
26-6 Types of Lenses Lenses are used to focus light and form images There are a variety of possible types We will consider only the symmetric ones the double concave and the double convex Recall prisms Bends light twice in the same direction Think of a convex lens as consisting of prisms light converges at a focal point (if properly shaped) Concave lens can also be modeled by prisms 10
Converging Lens Principal Rays Object F F P.A. Image 1) Rays parallel to principal axis pass through focal point. 2) Rays through center of lens are not refracted. 3) Rays through F emerge parallel to principal axis. Image is: real, inverted and enlarged (in this case). Assumptions: monochromatic light incident on a thin lens. rays are all near the principal axis. Diverging Lens Principal Rays Object F Image F P.A. 1) Rays parallel to principal axis pass through focal point. 2) Rays through center of lens are not refracted. 3) Rays toward F emerge parallel to principal axis. Image is virtual, upright and reduced 11
26-7: The Lens Equation We now derive the lens equation which determines the image distance in terms of the object distance and the focal length. Convergent Lens: h o f i h Ray Trace: Ray through the center of the lens (light blue) passes through undeflected. Ray parallel to axis (white) passes through focal point f. two sets of similar triangles: eliminating h /h: magnification: also same as mirror eqn!! M < 0 for inverted image. same as mirror eqn if we define i > 0 f > 0 Summary We have derived, in the paraxial (and thin lens) approximation, the same equations for mirrors and lenses: when the following sign conventions are used: Variable f > 0 f < 0 o > 0 o < 0 i > 0 i < 0 Mirror concave convex real (front) virtual (back) real (front) virtual (back) Lens converging diverging real (front) virtual (back) real (back) virtual (front) 12
3 Cases for Converging Lenses Object Image Past 2F Inverted Reduced Real This could be used in a camera. Big object on small film Object Between F & 2F Image Inverted Enlarged Real This could be used as a projector. Small slide on big screen Image Object Inside F Upright Enlarged Virtual This is a magnifying glass Lecture 18, ACT 5 A lens is used to image an object on a screen. The right half of the lens is covered. What is the nature of the image on the screen? (a) left half of image disappears (b) right half of image disappears (c) entire image reduced in intensity object lens screen 13
26-8 Dispersion and the Rainbow The index of refraction n varies slightly with the frequency f of light (or wavelength l) of light in general, the higher f, the higher the index of refraction n This means that refracted light is spread out in a rainbow of colors This is known as dispersion Prisms A prism does two things, 1. Bends light the same way at both entrance and exit interfaces. 2. Splits colors due to dispersion. Index of refraction 1.54 1.52 1.50 white light frequency ultraviolet absorption bands prism 14
Prisms Entering Exiting q 1 q 3 q 4 q 2 For air/glass interface, we use n(air)=1, n(glass)=n Prisms f The index of refraction for a material usually decreases with increasing wavelength Violet light refracts more than red light when passing from air into a material 15
Lecture 18, ACT 6 White light is passed through a prism as shown. Since n(blue) > n(red), which color will end up higher on the screen??? A) BLUE B) RED 26-8 Dispersion and the Rainbow Rainbows are created by the dispersion of light as it refracts in a rain drop. 16
26-8 Dispersion and the Rainbow How does it look. 26-8 More about Rainbows As the drop falls, all the colors of the rainbow arrive at the eye. 17
LIKE SO! In second rainbow pattern is reversed Sometimes a faint secondary arc can be seen. 26-8 A second Rainbow! Two reflection + refraction Less intense because of loss due to refraction 2017 Pearson Education, Inc. 18
26-8 The two Rainbows Why? 2017 Pearson Education, Inc. Recap of Today s Topic : Announcements: Team problems today Team 10: Alisha Kumar, Adam Saxton, Alanna Forsberg Team 11: Riley Burns, Deanne Edwards, Shauna Bolton Team 12: Kervell Baird, Matthew George, Derek Schultz Homework #8: due Friday Midterm 2: Tuesday April 10: covers Ch. 23-27. Office hours if needed (M-2:30-3:30 or TH 3:00-4:00) Chapter 26: Review of Refraction Total internal reflection Refraction and polarization Equation for lenses Dispersion & rainbows 19