1. Chapter 19 Optical Instruments

2. Contents The Camera: “Photography 101” The Human Eye The Magnifier The Microscope The Telescope Supplemental Topic: Resolution of Optical Instruments

3. The Camera “Photography 101”

4. The Simplest Camera: Pinhole Camera The chambered nautilius has a “pinhole eye” Photo taken with pinhole camera

5. A Lens Improves the Camera: 1.Lets in more light for brighter images. 2.Larger opening than pinhole provides more resolution (detail) 3.Lens allow focus control

6. Focusing a Camera Focusing: The lens is moved back and forth (varying s and s’) until the focused image is exactly on the film or detector

7. Digital Imaging and Pixels Pixel = “Picture Element” Camera detector is an array of rows and columns of pixels, like a checkerboard. Each pixel is a light-sensitive photodetector that converts light to electricity.

8. Pixels and Image Resolution More pixels = better resolution (detail) Modern Digital cameras contain millions of pixels (“Mega Pixels”). Inexpensive cameras often have more pixels than is needed. Image quality is limited by inferior optics (lens), not # of pixels.

9. Camera Exposure Control The exposure of the camera is controlled 3 ways: 1.Shutter: Covers the detector and opens up during the exposure. Duration is called “shutter speed” and ranges from 1/1000 second (bright light) up to several seconds (low light conditions). 2.Iris Diaphragm: Controls effective diameter of lens 3.ISO Sensitivity of the detector

10. The f-number The f-number is a measure of the light-gathering ability of the lens. Focal length: Longer focal length means larger image which spreads light out more: Dimmer image. Effective Lens Diameter: Larger iris diaphragm opening lets in more light: Brighter image. Notation: “f/4” means the f-number is 4: f/d = 4 To reduce the amount of light by factor of 2, need to “stop down” the lens (by making the iris smaller) such that its area is one half. Since A = π r², then A ~ d², so need to change d by factor of 1/√2. Thus f-number needs to change by factor of √2 = 1.41.

11. Exposure Control using f-stops Each “f-stop” number increases by factor of 1.4 which reduces the lens aperture (opening) area and thus amount of light by factor of 2.

12. Depth of Focus Higher f-numbers allow larger depth of focus (yellow region): 1.More margin, easier to focus. 2.Larger depth of field for objects in focus. f/2 f/8 f/2 The photographer can control the “depth of field” in his photo by choosing the f- number. f/8

13. ISO Exposure Control Before digital cameras were available, cameras used chemical-emulsion photosensitive film. Film sensitivity to light was measured by its ISO or ASA number. Modern digital cameras use these same ISO settings to adjust sensitivity of detector pixels. 100: Lowest sensitivity used for bright light conditions, best quality (least “grainy” due to lowest level of electronic “noise”) 200: Twice as sensitive to light, but twice as grainy 400: Four times as sensitive (requires 4X shorter exposure) 800: 1600: 3200: Highest sensitivity used for extreme low-light conditions, but image’s electronic noise is also amplified (most grainy)

14. The Human Eye

15. The Eye works like a Camera Lens: Focuses light (along with cornea) like camera’s lens. Iris: Size varies to adjust amount of light entering eye like camera diaphragm. Retina: Light-sensitive cells convert image into electrical nerve impulses (similar to camera detector pixels) Eyelid: Opens/Closes like camera shutter.

16. Focusing and Accommodation Accommodation: The process by which the eye changes the shape of its lens to focus on objects at different distances. This is different than focusing a camera where the distance between the lens and detector is varied.

17. Why is our vision blurry Underwater? Seeing in air works well because large difference of indices of refraction between air and cornea: Cornea able to refract rays. Seeing underwater (without goggles or mask) is difficult because water and cornea have similar indices of refraction: Minimal refraction of incoming rays occur. Goggles or mask provide layer of air on cornea: Perfect vision!

18. The Far Point and Near Point Far Point (FP): The farthest distance that the relaxed eye can focus on. Normal vision far point is infinity. Near Point (NP): The closest distance the eye can focus on. Varies with age from 10 cm (young kids) to >100 cm for elderly. Typical value is 25 cm for young adults.

19. Vision Defects Hyperopia (Far sighted) Eyeball too short Myopia (Near sighted) Eyeball too long

20. Correcting Hyperopia Example: Ryan’s near point is 150 cm instead of 25 cm. What eyeglasses will an optometrist prescribe? We want the eyeglasses to allow Ryan to see objects as close as 25 cm (the normal vision near point). But Ryan’s eyes can only focus on objects as close as 150 cm. Thus we want the glasses to form a virtual image (of an object at 25 cm) at 150 cm that becomes the object for the eye.

21. Correcting Myopia Example: Kasey’s far point is 200 cm instead of infinity. What eyeglasses will an optometrist prescribe? We want the eyeglasses to allow Kasey to see objects at infinity (the normal vision far point). But Kasey’s eyes can only focus on objects as far as 200 cm. Thus we want the glasses to form a virtual image (of an object at infinity) at 200 cm that becomes the object for the eye.

22. Refractive Power and Diopter units Previous examples: Ryan Kasey

23. The Optometrist’s Eyeglass Prescription

24. The Magnifier

25. Apparent Size Consider the “Little Man” and his BIG GIRLFRIEND Why does she look so much bigger than him??

26. Apparent Size and Angular Size She appears bigger because she is closer to the camera. Her apparent size is larger than his. Her angular size is also larger: She subtends a larger angle. Larger angular sizes appear bigger to us.

27. Example: Calculate Angular Size of the Sun Recall geometry of a circle:

28. The Magnifier (Magnifying Glass)

29. The Magnifier: Placing the object inside the focal point Draw 3 special rays from tip of object: 1) Parallel ray bends thru the far focal point. 2) Ray extended thru near focal point emerges parallel to axis. 3) Ray thru center of lens does not bend. 1 2 3

30. The Magnifying Glass A converging lens becomes a magnifying glass when the object is inside the focal point. Magnifications up to about 20X are possible.

31. The Magnifier Angular size without a magnifier Angular Magnification: Angular size with a magnifier

32. Where is the Magnified Image? Suppose we place the object right at the focal point. Use the lens equation: Since s = f: Solve for s’:

33. The Microscope

34. Combinations of Lenses Many optical instruments use more than 1 lens. The image of the first lens becomes the object for the second lens. If a 3 rd lens is used, the image of the 2 nd lens becomes the object for the 3 rd lens, etc.

35. The Microscope Much more powerful than a magnifying glass because 2 lenses are used: Objective lens and eyepiece lens. Magnifications up to 2000X are possible.

36. The Microscope 1. The objective lens first produces a magnified real image of the tiny object being studied. 2. The eyepiece lens then magnifies the real image, producing a virtual image at infinity.

37. Microscope Magnification Chap. 18 (Magnifier)

38. Example: Microscope Magnification A standard microscope has a tube length of 160 mm. Suppose the objective’s focal length is 8 mm and the eyepiece focal length is 10 mm. Find the magnification.

39. The Telescope

40. Refracting and Reflecting Telescopes Refracting telescope: Lens focuses light onto the focal plane Reflecting telescope: Concave mirror focuses light onto the focal plane Focal length

41. My Homebuilt 18” Reflecting Telescope 18” Primary Mirror Homebuilt mounting Computerized tracking Total cost ~$8000

42. Hale Telescope (Palomar Mountain) Mirror is 200 inches (5 meters or 17 feet) diameter

43. The Keck Telescope (Mauna Kea, Hawaii) Segmented mirror is 10 meters (33 feet) diameter

44. The Refracting Telescope

45. Telescope Magnification As with all optical instruments, the angular magnification is determined by geometry: Triangles and small-angle approximations. Angular size with naked-eye: Angular size thru telescope:

46. The 3 Powers of a Telescope 1.Light Gathering Power 2.Resolving Power 3.Magnifying Power

47. Light Gathering Power: Size Does Matter! 1. Light-gathering power: Depends on the surface area A of the primary lens or mirror, proportional to diameter squared: A =  (D/2) 2 D Example: Find the light-gathering power of a 3-inch diameter (76 mm) telescope compared to the unaided human eye, which has a pupil diameter of 8 mm. Telescope area  (D/2) 2 (76) 2 -------------------- = ------------ = ------ = 90 times Pupil area  (D/2) 2 (8) 2

48. Telescope Diameter vs Light-Gathering Power Small Medium Large Telescope Telescope Telescope

49. Resolving Power of a Telescope Due to the wave nature of light, the telescope itself produces wave interference called “diffraction rings” around the image: Actual Star image (greatly magnified) Actual Image of 2 stars close together Ideal Star image Ideal image of 2 stars close together Telescope has difficulty resolving the 2 stars

50. Resolving Power of a Telescope (2) Small telescope Medium telescope Large telescope The larger the telescope aperture (diameter), the smaller the diffraction rings: Larger telescopes produce sharper images: Higher resolution, more resolving power

51. Telescope Diameter vs. Resolution 6” 12” 18” Telescope Telescope Telescope More resolving power Larger telescopes produce sharper images: Higher resolution, more resolving power

52. The Powers of a Telescope (3) 3. Magnifying Power = ability of the telescope to make the image appear bigger. The magnification depends on the ratio of focal lengths of the primary or “objective” mirror/lens (F o ) and the eyepiece (F e ): A larger magnification does not improve the resolving power of the telescope!

53. How Eyepiece Size Effects Magnifying Power

54. Supplemental Topic: Resolution of Optical Instruments

55. Circular Aperture Diffraction Telescopes, microscopes, binoculars have light coming thru a circular opening (aperture), producing a diffraction pattern: Central maximum and diffraction rings.

56. Resolution Limits of a Telescope Due to the wave nature of light, the telescope itself produces wave interference called “diffraction rings” around the image: Actual Star image (greatly magnified) Actual Image of 2 stars close together Ideal Star image Ideal image of 2 stars close together Telescope has difficulty resolving the 2 stars

57. Circular Aperture Diffraction

58. Effect of Aperture on Diffraction Rings Small telescope Medium telescope Large telescope The larger the telescope aperture (diameter), the smaller the diffraction rings: D = Diameter of telescope (aperture) Larger telescopes produce sharper images: Higher resolution, more resolving power

59. Telescope Diameter vs. Resolution 6” 12” 18” Telescope Telescope Telescope More resolving power Larger telescopes produce sharper images: Higher resolution, more resolving power

60. Rayleigh’s Criterion for Resolution Two objects are resolvable if they are separated by an angle θ greater than θ = 1.22λ/D. This angle occurs when the central maximum of one image lies directly over the first minimum of the 2 nd image.