Geometrical Optics

1. Geometrical Optics 14.2

2. Getting There Fast – Are you studying for the final yet??

3. This week • This week we will cover some topics in geometrical optics. This will include mirrors and lenses. This is about all that we will be able to accomplish. • Only what we cover in class will be covered on the final examination. • There will be NO QUIZ this week. • The final exam will be on Saturday, April 30th in room HPA 119. (Two Index Cards allowed) • Entire semesters work. • Joint exam with other Studio Class. • Watch for new WebAssign and probably one after that.

4. Next Week • Monday • Post Test (will be used for borderline cases) • Complete topics and possibly some problems • Wednesday-Friday • If there is coordinated interest, I might be able to come to campus and go over some problems. Need to find some common day/time to do this. • Saturday • Final Examination (2 index cards allowed).

5. About the final examination • Only topics discussed • In class, • On class PowerPoint lectures • Contained in the lab sheets, • Included in WebAssigns or • Assigned for reading • will be covered on the final exam. • That’s a lot of stuff!

6. NOTICE: Bring ALL Lab Unitsfrom Magnetism Through Optics to class on Friday. One of them will be collected for grading. STUDIO UNIT ???

7. Geometrical Optics Yup … more angle stuff!

8. Geometrical Process Object Image Lens or Mirror

9. Where’s the image, where’s the object … who cares??? We do! • What kind of an image is it? • Real • Virtual • Where is the object, where is the image? • Behind the mirror • In front of the mirror • Where is the light coming from? Where is it going? • What is the size of the image? (magnification) • What is the orientation of the image? • Same as the object, • Inverted (upside down) • Reverse Questions about the image:

10. What kind of optics: mirrors • Mirror • Planar • Concave • Convex • Lens • converging • diverging • Where is the light? • Have you seen the light yet?

11. Note • The object is usually the source of light. • The image is where the light converges to replicate the object. • The image can be on either side of the “optical element” • The image can be real or virtual • The image can form an object for a second optical element. • Yes .. it can be confusing. We will attack this a point at a time. You have done some of this in the units so this is a review of sorts.

12. Signs – We mean (-) or (+) • The distance from the object to the lens/mirror is called the object distance. • It is positive if it is on the same side of the optical element as the incoming light. Otherwise it is negative • It is designated by s • The distance from the image to the lens/mirror is called the image distance. • It is positive if it is on the same side as the outgoing light • It is designated by s’. Otherwise it is negative. • Without this sign convention, these problems would be much more difficult. So pay attention to them!!

13. Consider looking in a plane mirror in your bathroom. Your image distance is • Positive • Negative • This convention doesn’t apply to my bathroom mirror.

16. Paraxial Rays : Small Angle Approximation

17. M I r r o r P l a n e

19. Curved Mirrors For Student Misery Only!

20. Concave Mirror con-CAVE

21. Sign Convention When the Center of Curvature is on the same side of the outgoing ray, R is positive. Otherwise, if the center of curvature is not on the same side as the outgoing ray, R is negative.

22. Concave Mirror/Paraxial Approximation The normal to the surface passes through C Therefore Consequently MIRROR EQUATION

23. For this structure • The Radius R is positive and s’ is negative • The Radius R is negative and s’ is negative • R is positive and s’ is positive • R is negative and s’ is positive Answer

24. When the Center of Curvature is on the same side of the outgoing ray, R is positive. the image distance is positive if it is on the same side as the outgoing light

25. This image is • real, reversed • virtual, not reversed • real, not reversed • virtual, reversed

26. What about here? R, s, s’ (convex mirror)

27. Concept: Focal Length of a Mirror

28. Going Backwards

29. For a convex mirror, the Radius • Is positive • Is negative • The sign depends on the position of the image. • The sign depends on the current sign of the zodiac.

30. R When the Center of Curvature is on the same side of the outgoing ray, R is positive. Otherwise, if the center of curvature is not on the same side as the outgoing ray, R is negative.

31. Image Formation – Ray Diagram ‘ ‘ y’<0 (from the diagram) so image is inverted.

32. Continue the current Unit

33. Examples to review

34. A concave spherical mirror has a radius of 10 cm. Calculate the location and size of an 8mm object a distance 15 cm from the mirror. 10 cm 5 cm Normal to mirror and bounces back along incoming path.

35. A concave spherical mirror has a radius of 10 cm. Calculate the location and size of an 8mm object a distance 10 cm from the mirror. 10 cm 5 cm

36. A concave spherical mirror has a radius of 10 cm. Calculate the location and size of an 8mm object a distance 2.5 cm from the mirror. virtual image 10 cm 5 cm eye

37. The Concave Mirror The Equations are the same as the convex mirror but the Radius of the mirror is negative

38. More Convex Mirror

39. Graphical Methods are very useful to check your work.