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 1

o i f h’ h 26.5

EM wave at an interface What happens when light hits a surface of a material? Three Possibilities Reflected Refracted (transmitted) Absorbed Snell’s Law q2 q1 incident ray reflected ray qr MATERIAL 1: n1 MATERIAL 2: n2 refracted ray

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 n1 = n2 Þ no effect If light enters normal Þ no effect

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

Lecture 18, ACT 2 (a) (b) (c) (d) 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 (n1=1.5) to air (n2=1.0) incident ray reflected refracted q2 q1 qr GLASS AIR n2 n1 ie light is bent away from the normal. as q1 gets bigger, q2 gets bigger, but q2 can never get bigger than 90° !! In general, if sin q1  sin qC  (n2 / n1), we have NO refracted ray; we have TOTAL INTERNAL REFLECTION. For example, light in water which is incident on an air surface with angle q1 > qc = sin-1(1.0/1.5) = 41.8° will be totally reflected. This property is the basis for the optical fibers used in communication.

ACT 3: Critical Angle... 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. Compare the critical angles for total internal reflection in these two cases a) qcI>qcII b) qcI=qcII c) qcI<qcII air n =1.00 glass n =1.5 qc water n =1.33 Case I Case II

ACT 4: Fiber Optics 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 air n =1.00 glass n =1.5 qc water n =1.33 Case I Case II

© 2017 Pearson Education, Inc. 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”

Fiber Optics An application of internal reflection Plastic or glass rods are used to “pipe” light from one place to another 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 90o Polarization is parallel to the reflecting surface Applications Remove reflection Photographs of objects in water …

© 2017 Pearson Education, Inc. 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.

q R h q R-i o-R h’ i o & h i o f h’

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 g q a object b h image o i

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

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

Converging Lens Principal Rays F Image P.A. Object F 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 F P.A. Image Object F 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

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: o h i f 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: same as mirror eqn if we define i > 0 f > 0 eliminating h’/h: magnification: also same as mirror eqn!! M < 0 for inverted image.

when the following sign conventions are used: 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) Lens converging diverging real (back) virtual (front)

3 Cases for Converging Lenses Object Image Past 2F Inverted Reduced Real This could be used in a camera. Big object on small film Image Object Between F & 2F 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) left half of image disappears object 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? lens (a) left half of image disappears (b) right half of image disappears screen (c) entire image reduced in intensity

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, Index of refraction frequency ultraviolet absorption bands 1.50 1.52 1.54 A prism does two things, Bends light the same way at both entrance and exit interfaces. Splits colors due to dispersion. white light prism split into colors!

For air/glass interface, we use n(air)=1, n(glass)=n Prisms q1 q2 Entering q3 q4 Exiting 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

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.

26-8 Dispersion and the Rainbow How does it look …. Figure 35.24 The formation of a rainbow seen by an observer standing with the Sun behind his back.

26-8 More about Rainbows As the drop falls, all the colors of the rainbow arrive at the eye.

Sometimes a faint secondary arc can be seen. LIKE SO! In second rainbow pattern is reversed Sometimes a faint secondary arc can be seen.

© 2017 Pearson Education, Inc. 26-8 A second Rainbow ! Two reflection + refraction Less intense because of loss due to refraction © 2017 Pearson Education, Inc.

© 2017 Pearson Education, Inc. 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