1. Physics 52 - Heat and Optics Dr. Joseph F. Becker Physics Department San Jose State University © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

2. Chapter 34 Geometrical Optics © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

3. Light rays radiate from a point object in all directions. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

4. The rays entering the eye after reflection from a plane mirror look as though they had come from point P’, the image point for the object P. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

5. Refraction at a plane interface (n a > n b ). The image P ’ is closer than P. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

6. Reflection from a plane mirror. P’ is a virtual image. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

7. Reflection of an object (y) from a plane mirror. Lateral magnification m = y ’ / y © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

8. SIGN RULES FOR ALL REFLECTION AND REFRACTION SITUATIONS 1.SIGN RULE FOR THE OBJECT DISTANCE: When the object is on the same side of the reflecting or refracting surface as the incoming light, object distance s is positive; otherwise it is negative. 2.SIGN RULE FOR THE IMAGE DISTANCE: When the image is on the same side of the reflecting or refracting surface as the outgoing light, the image distance s’ is positive; otherwise negative. 3.SIGN RULE FOR THE RADIUS OF CURVATURE OF A SPHERICAL SURFACE: When the center of curvature C is on the same side as the outgoing light, radius R is positive; otherwise it is negative. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

9. The image formed by a plane mirror is virtual, erect, and reversed. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

10. Construction for finding image of a concave spherical mirror. The image is real, inverted, and magnified. (angle of incidence = angle of reflection, or  =  )  tan  ~  etc. so  = h / s,  = h / s’,  = h / R  1/s + 1/s’ = 2/R © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

11.  =  =  =  tan  ~  etc. so  = h / s,  = h / s’,  = h / R  =  h / s + h / s’  = h / R 1/s + 1/s’ = 2/R

12. A concave spherical mirror causes rays parallel to the axis to converge at the focal point F. For s = oo 1/oo + 1/s’ = 2/R and s’ = R /2 = f where f is the focal length of the mirror © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

13. Image position and height formed by concave spherical mirror: m = y ’ / y = - s ’ / s © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

14. The concave mirror forms a real, enlarged, inverted image of the lamp filament. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

15. Finding position and size of image formed by convex spherical mirror. 1/s + 1/s ’ = 2/R; m = y ’/ y = - s ’/s © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

16. Convex spherical mirror (a) Incident rays parallel to axis. (b) Incident rays aimed at the virtual focal point F. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

17. Principal-ray diagrams: graphical method of locating the image formed by a spherical mirror. Principal rays: 1. Ray parallel to the axis. 2. Ray thru the focal point F. 3. Ray along the radius. 4. Ray to the vertex V. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

18. Principal-ray diagrams: graphical method of locating the image formed by a spherical mirror. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

20. Refraction at a spherical surface – position of image. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

21.  a  =  =  b tan  ~  etc. so  = h / s,  = h / s’,  = h / R Snell’s Law: n a sin  a = n b sin  b n a  a = n b  b  b = (  ) n a / n b n a  + n b  =  n b  n a  n a /s + n b /s’ = (n b - n a ) / R (Continued) Refraction at a spherical surface – position of image. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

22. Refraction at a spherical surface – height of image. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

23. A glass rod in air forms a real image inside the rod. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

24. First and second focal points of a converging thin lens. The numerical value of f is positive. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

25. Construction used to find the image position for a thin lens. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

26. First and second focal points of a diverging thin lens. The numerical value of f is negative. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

27. Lensmaker’s equation for a thin lens: 1 / f = (n – 1) (1 /R 1 - 1 /R 2 ) © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

28. Principal-ray diagrams showing the graphical method of locating an image formed by a thin lens (converging and diverging). © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

29. Formation of images by a thin converging lens for various object distances. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

30. Principal-ray diagram for an image formed by a thin diverging lens. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

31. The real image of the first lens acts as the object for the second lens. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

32. acts as a virtual object for the second lens. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics The image produced by first lens

33. OPTICAL INSTRUMENTS Camera The Eye Magnifier Microscope Telescope © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

34. A typical single lens reflex camera. The lens has many elements cemented together to form a single compound lens. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

35. The larger image size with a larger value of f corresponds to a smaller angle of view. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

36. In a camera lens, larger f-numbers mean smaller aperture diameters. “f-number” = f / D where D = diameter of the aperture © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

37. Principle of zoom lens: use two elements with variable spacing. The effective focal length depends on the distance between the two optical elements. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

38. Overhead projector. An inexpensive plastic Fresnel lens is like an ordinary thick lens with the internal material removed. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

39. The eye. The muscle contracts to change the focal length of the lens to image close objects.

40. Normal eye myopic (nearsighted) eye hyperopic (farsighted) eye © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics Dashed blue curve is correct position of the retina.

41. Vertical lines are imaged in front of this astigmatic eye. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

42. A diverging cylindrical lens images the vertical line on the retina of this astigmatic eye. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

43. ( a) An uncorrected hyperopic (farsighted) eye. (b) A positive (converging) lens gives the extra convergence needed for a hyperopic eye to focus the image on the retina. The virtual image formed by the converging lens converging lens acts as an object at the near point.

44. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics (a) An uncorrected myopic (nearsighted) eye. (b) A negative (diverging) lens spreads the rays so that the myopic eye can focus the image on the retina. The virtual image formed by the diverging lens acts as an object at the near point.

45. The magnifier : (a) The subtended angle  (angular size) is largest when the object is at the near point. (b) The magnifier gives a virtual image at infinity. The virtual image appears to the eye to be a real object subtending a larger angle  ’ at the eye. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics s = f F2F2 M =  ’/  = (y/f)/(y/25) M = 25/f

46. (a) Elements of microscope. (b) Object is very close to the objective lens. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

47. LIGHT  MICROSCOPE IMAGE EYE OBJ. m = -s’/s = -s 1 ’/f 1 M TOTAL = (-s 1 ’/f 1 )(25/f 2 ) © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

48. Astronomical refracting telescope. Distant object has a real inverted image.

49. TELESCOPE OBJECT AT INFINITY LIGHT  M =  ’/  = (-y’/f 2 )/(y’/f 1 ) M = -f 1 /f 2 © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics

50. Inversion of an image in prism binoculars.

51. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics Optical systems for reflecting telescopes. (a) prime focus, (b) Newtonian, (c) Cassegrain.

52. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics Spherical aberration for a lens. The “circle of least confusion” is shown by C.

53. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics Astigmatism for a lens for a point below the optic axis. The lens forms two images of the point, in planes perpendicular to each other.

54. © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics Focal length of a zoom lens: f = f 1 |f 2 |/(|f 2 |-f 1 +d)

55. Review © 2005 J. F. Becker San Jose State University Physics 52 Heat and Optics