1. Geometrical Optics – Part II Chapter 24 1

2. Going Backwards 2

3. Stuff  We continue with mirrors and lenses and even refractive surfaces.  Quiz on Friday  For a while, office hours will be in, of all places, my office. We really don’t need MAP-318 except before exams. And the hours are too confusing.  Next Exam is on Wednesday, December 2 nd.  I give up on the remaining evil clickers. Clicker grade=0.  Let’s move on. 3

4. 4 When the Center of Curvature is on the same side of the R outgoing ray, R is positive. Otherwise, if the center of curvature is not on the same side R as the outgoing ray, R is negative.

5. Concave Mirror/Paraxial Approximation Consequently MIRROR EQUATION 5

6. Image Formation 6 ‘ ‘ y’<0 (from the diagram) so image is inverted.

7. The geometry…… 7

8. Let’s try an example 8

9. 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. 9 10 cm 5 cm Normal to mirror and bounces back along incoming path.

10. 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 10 cm 5 cm

11. 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. 11 10 cm 5 cm eye virtual image

12. The Concave Mirror 12

13. More Convex Mirror 13

14. Graphical Methods are very useful to check your work. 14

15. Moving on to refractive surfaces 15

16. Spherical Refractive Surfaces 16 air glass

17. A closer look at the Math …. 17

18. No for the height of the image 18

19. Check this out – how big is R? 19

20. From the math: 20

21. 21

22. The Thin Lens  We ignore the thickness of the lens.  We will use mostly geometrical methods.  Any ray that bends is assumed to bend only once at the center of the lens. 22

23. From whence it came 23 Surface 1 Surface 2 n=1 n=1.5 n=1 Surface 2 n>1

24. The thin lens - geometry 24 parallel

25. More Geometry  Lens is thin  Actual thickness of the lens is ignored.  Image from first surface provides the object for the second surface.  Paraxial Ray Approximation  sin(x)=tan(x)=x  cos(x)=1  x is in RADIANS 25

26. More Geometry 26 Triangle PQO and triangle P’Q’O are similar. We will show that for a very thin lens: F 1 =F 2 =f The Thin Lens Equation

27. 27 This, of course depends on where the object is placed with respect to f.

28. Thin Lens (con’t) 28 Image that would form if material “a” was all on this side of the lens. Object for second surface.

29. 29 Procedure for equation Solve for image position for first surface Use image as object for the second surface. Use the refraction equation in both cases. For a lens. n a =n c =1 So we can call the middle one just n Mess with the algebra and you will get:

30. FINALLY – with some algebra and obvious substitutions, we get: 30 The Lensmaker’s Equation

31. Two Ways to do this STUFF  Algebraically using the lens equation (with the 1/f if you know it)  Using graphical Methods 31

32. Graphical Methods: 32

33. Graphical Methods: 33

34. Most important case: converging lens Object to left of F1 34

35. Most important case: converging lens 35

36. Most important case: converging lens 36

37. Most important case: converging lens 37

38. Most important case: converging lens 38

39. Most important case: converging lens 39