Physics 1230: Light and Color Ch. 3: Mirrors and Lenses Ivan Smalyukh

1. Building on concepts from the last chapter Now that we know how rays and images work we can understand how curved mirrors and lenses produce images Practical applications include magnifying mirrors, rear-view mirrors, glasses and contact lenses, and cameras. Spherical mirrors Significance of focal point Tracing reflected rays to find virtual images in convex mirrors Tracing reflected rays to find virtual and real images in concave mirros Lenses Significance of focal points, focal lengths, focal planes and power of a lens Tracing rays to find images from thin convex and concave lenses. Fresnel lenses Compound lenses and using intermediate images to find final images Physics 1230: LightandColorCh. 3:Mirrors and LensesIvan Smalyukh

5. A convex mirror bulges outwards towards you What is a spherical convex mirror? (Think of the rear view mirror on your car) Reflecting surface ofconvex spherical mirror Axis of mirror Center of sphere

6. Virtual imageon other side of mirror iscompressedvertically Virtual imageon other side of mirror isstretchedvertically Mirrors curved like a cylinder can make you look fat or skinny Looking at yourself in a convex mirror, the image is compressedvertically like rear view mirror but in one dimension only. Your image looks fat Looking at yourself in a concave mirror, the image isvertically expandedlike a bathroom magnifying mirrorbut in one dimension only. Your image looks skinny

7. The center of the sphere (circle) is in front of the mirror The focal length is also in front of the mirror, halfway between the center and the mirror surface A concave mirror bulges away from you Mirror surface Axis Focalpoint Center

8. Convex mirror Rays which arrive at the mirrorfrom a close source, like Alex’snose are not almost parallel Why are the rays from a distant light source such as the sun or a star essentially parallel? Here the rays from a distant light sourcesuch as the sun By the time they arrive here(into a camera or mirror) onlythe nearby almost parallel rays enter Convex mirror Whenever we speak of incoming parallel rays you can always visualize rays from the sun or a star.

16. http://micro.magnet.fsu.edu/primer/java/mirrors/concavemirrors/index.htmlhttp://micro.magnet.fsu.edu/primer/java/mirrors/concavemirrors/index.html http://micro.magnet.fsu.edu/primer/java/mirrors/convexmirrors/index.html http://micro.magnet.fsu.edu/primer/java/mirrors/convexmirrors3d/index.html http://micro.magnet.fsu.edu/primer/java/mirrors/concave.html

17. http://micro.magnet.fsu.edu/primer/java/mirrors/convex.html

19. Where is Alex's image when he is between the center and it's focal point? Let's find the image of his nose Here is a ray of type 1 from his nose reflecting off the mirror Here is a ray of type 3 from his nose reflecting off the mirror The image of the nose is at the intersection of reflected rays of type 1 and type 3. Why? Can we use a ray of type 2? Here is Alex's image Is it (a) real or (b) virtual? Magnified or reduced? From which points can your eye see his nose? From all points (A, B, C)? From A and C, but not B? From B and C, but not A? From A only? From C only Here is how we use those rays to find the image of an object in a concave mirror Mirror surface Axis Center Focalpoint A C Clicker Question B

20. Here are rays 1 and 3 used to find the image Alex's nose Here are some other (less convenient) incident and reflected rays They all go through the same image point as rays 1 and 3 after satisfying the law of specular reflection! Any two rays from an object point will intersect at the image point but rays 1, 2 and 3 are the easiest to use to find the image point Special rays 1, 2 and 3are not necessary to find the image of an object but are easier to work with than others

21. Draw rays of type 1 and type 3 from his nose to the mirror The reflected rays will never intersect behind Alex since they diverge behind him However we can extend the reflected rays behind the mirror where they do intersect The image of Alex's nose is at the intersection of the backward extended reflected rays Is it real (a) or virtual (b)? Reduced (a) or magnified (b)? Right side up (a) or inverted (b)? What happens to his image if Alex is closer to the mirror than the focal point? Mirror surface Focalpoint Center • Here is the whole image • This is a magnifying mirror (for shaving or cosmetics) Clicker question

22. Informatiuon • HW # 4 due on Thursday, Sept. 24 • Exam #1 on Tuesday, September 29 – Chapters 1-3 of the textbook; • Exam preparation: http://www.colorado.edu/physics/phys1230/phys1230_fa09/Exams.htm • On Thursday: questions/answers & exam #1 material overview + new material

23. HW#2

24. Concept question • Is your make-up/shaving mirror • Flat • Concave • Convex

25. Lenses

30. The focal point of a mirror was at the image point of a distant star (or the sun) seen in that mirror This is true for both convex mirrors (virtual image of star) and for concave mirrors (real image of star). The reason for involving the sun or a distant star is to guarantee that the incoming rays are essentially parallel. The same is true for lenses The converging lens of a magnifying glass brings the sun’s (parallel) rays to a focus at the “hot spot” which can produce a fire. The location of the hot spot is at the focal point of the lens. (Parallel) rays from the sun Converging lens Focal length Focal point Focal point of a converginglens is where image of a distant object (sun) lies

31. Here is a converging lens with its axis and BOTH focal points shown Both sides of a converging lens bulge outwards Parallel incoming rays are refracted so that they ALL pass through the focal point F' This fact defines F' and can be used to find its location! Rays diverging from F and passing through the lens ALL come out parallel Unlike a mirror there are two focal points of a lens, one on either side Incoming ray is benttowards nornal Outging ray is bentaway from nornal F F' F F'

32. Do we have to draw a to-scale ray-tracing for each different object location to find the image location? No, you don't have to do any ray-tracing at all (Thank goodness!!) But you have to use some algebra The distance between the center of the lens and either F or F' is the same. It is called the focal length, f F' F Can we be more precise with distances and magnifications? These distances are theSAME. Either one iscalled the focal length, f

33. The image produced by a thin converging lens whose axis and focal points are known can be found by replacing the lens by a plane through its center A ray of type 1 goes from Alex's nose parallel to the axis to the plane and then refracts through the focal point F' A ray of type 2 goes from his nose through the center of the lens (plane) The image of the nose is at the intersection of the two rays You can check your results with a ray of type 3which goes from his nose through focal point F and then parallel to the axis F' F How to use rays of type 1, 2 and 3 to find the image produced by a thin converging lens Is the image upside down or right side up? Use the axis to help determinethe image by locating its bottom!

34. We draw incident and transmitted rays of type 1 and 2. Note that the transmitted (bent) rays diverge on the other side of the lens so the image cannot be there. Try extending the transmitted rays backwards. The image is where they intersect Note rays of type 3 are in agreement with the image point determined by rays 1 and 2 even though they don't pass through the lens! Is it inverted (a) or right-side-up (b)? Is it magnified (a), reduced (b) or unchanged (c) in size? F' F Where is the image when Alex is close to the converging lens (closer than F)? This is a magnifying glass!!

35. F' F' F F Compare the results of ray tracing to find an image of Alex for each of his two positions. Alex is further from the lensthan the focal point F Image is real Alex is closer to the lensthan the focal point F Image is virtual

36. Each image point is now scattered from the screen in all directions Hence, you eye can see the image not only by looking into rays 1, 2 and 3, but also by looking at the screen into the new (scattered) rays We can even see the image from the other side of the screen since rays are scattered there too! F' F What happens if we put a translucent screen at the location of the real image? New rays scattered off translucentscreen particles at each point

38. A diverging lens has concave surfaces (one or both) The focal points on a diverging lens are reversed. Parallel incoming (type 1) rays come out the other side diverging as though they came from the first focal point which is called F'. Incoming (type 3) rays aimed at the focal point behind the lens (F) come out parallel Diverging lenses deflect rays so that they point further away from the axis F' F F How does a diverging lens differ from a converging lens? Incoming ray is benttowards nornal Outging ray is bentaway from nornal F'

40. Computer simulation of light focusing/defocusing by lenses: http://micro.magnet.fsu.edu/primer/java/lenses/converginglenses/index.html http://micro.magnet.fsu.edu/primer/lightandcolor/lenseshome.html http://micro.magnet.fsu.edu/primer/java/lenses/simplethinlens/index.html http://micro.magnet.fsu.edu/primer/java/lenses/diverginglenses/index.html http://micro.magnet.fsu.edu/primer/java/components/perfectlens/index.html

43. See the following online interactiveexperiment to learn the answer As a pencil moves closer to a converging lens what happens to its image? http://www.colorado.edu/physics/phet/simulations/lens/lens.swf

44. Sept 24