HW3

1. HW3 • Grading scale for homeworks - will be adjusted to %.

2. HW4 • HW #5 is assigned today – see the course web page; • Monday Morning - Exam grades available in CULearn.

3. The Camera and Photography Using what we have learned about lenses and ray-tracing to understand: Cameras with lenses versus pinhole cameras Focusing, depth of focus and depth of field Telephotos and wide-angle lenses "New" subjects in photography Parts of the camera The shutter, speeds and motion blur The diaphragm, aperture control, stops and f-numbers Exposure Physics 1230: LightandColorChapter 4

4. blocked rays A pinhole camera works by blocking rays • What is an image? • A real image is formed on a screen when rays from each point on the object reach the corresponding points on the screen and no other rays from other points on the object reach those points Pinhole Camera Image oflight bulb Light bulb

5. blocked rays The object photographed with a pinhole camera does not have to be self-luminous! One of many rays of light shining on Alex Pinhole Camera Rays from the real Alex go through the hole and make the image Image ofAlex Alex

6. Why we do not use such a simple camera? • (A) Not very bright images; • (B) Focusing is difficult; • (C) Because of spherical aberrations; • (D) A, B, & C • (E) none of the above;

7. previously blocked rays If a lens is used instead of a pinhole the image is brighter because many of the previously blocked rays are bent so that they arrive at the correct place on the screen image Camera with lens Pinhole Camera blocked rays Image of light bulb Light bulb Not just ONE ray from the filament but MANY now arrive at the corresponding image point so the image is BRIGHTER

8. As the distance between the pinhole and the back of the pinhole camera is increased the image increases in size This is a telephoto effect The image ALWAYS STAYS IN FOCUS (sharp) because for a pinhole camera there is only one ray connecting each object point to each image point A telephoto effect (enlarged image) for a pinhole camera only requires increasing the distance from pinhole to camera back

9. As the distance between the lens and the back of the camera is increased the image remains in the same place It is no longer in focus at the back of the camera It is in focus at the same place as before x0and f are the same so xi must be at the same place In addition to increasing the distance between the lens and the back of the camera the focal length of the lens must be increased by the right amount! The new image is larger and in focus f f fnew A telephoto effect (enlarged image) for a camera with a LENS requires increasing the distance from lens to camera back AND increasing the focal length of the lens to keep the image in focus

10. For most of us these days a zoom lens is used whose focal length can be adjusted and changed Advanced photographers use interchangeable lenses with different focal lengths for different effects A telephoto effect is achieved in cameras in a variety of ways • The distance, xi, from the lens to the back of the camera must be adjusted for each different focal length • xi must = that special distance at which rays from an object point all come together (intersect) at image point • This is called focusing • For other distances, xi, the image at the camera back is said to be out of focus • Interact with the lens

11. Single-lens reflex Point and shoot digital Parts of camera illustrated

12. Back of camera where film or CCD (for digital camera) goes Lens - it can always be moved closer to the camera back or further from the back. This is called focusing The lens can have a fixed focal length or can have a variable focal length (zoom) Diaphragm - this decreases the usable diameter of the lens in steps Shutter - The shutter lets light from an object reach the lens and the film (or CCD) for a limited, controlable time The shutter and diaphragm together control how much light reaches the camera back They control the exposure On automatic cameras adjustment of the exposure (diaphragm/shutter) is done automatically. Parts of a camera

13. Single-lens reflex Point and shoot digital Parts of camera illustrated

14. The depth of focus is the range of lens to camera-back positions at which the image is tolerably sharp (in focus) This range is infinite for a pinhole camera because the image is always in focus (one ray connects each object pt to each image pt) For a lens camera the depth of focus depends on the diameter of the lens its focal length and the object distance The circle of confusioncontains the rays that focus to a point elsewhere If the diameter of the circle of confusion is small enough the blur is tolerable when the camera back is there A lens with smaller diameter has a larger depth of focus because it is more like a pinhole (image is dimmer) imageblurry herebut tolerable depth of focus f circles ofconfusion f missing ray smallercircle ofconfusion What is the depth of focus of a lens in a camera?

15. Depth of field is related to depth of focus It is the maximumdistance along the axis by which two objects can be separated and still be reasonably in focus Deep focus is the term for large depth of field in movie-making The depth of field of a pinhole camera is infinite because all objects are in focus at all lens-camera back locations A smaller lens opening (aperture) gives a larger depth of field but a dimmer image Wide angle lenses generally have more depth of field than telephotos Depth offield diameter of circle of confusion(maximum tolerable blur) What is the depth of field of a lens?

20. Exam #1: Average = 81.8

21. The diameter of the aperture of a lens can be reduced by means of the diaphragm. The largest aperture is the full diameter of the lens Smaller apertures are called stops The aperture is measured by the f-number = focallength of the lens divided by the diameter of the aperture: f-number (or f-stop) = f/d Hence, a large f-number means a small lens diameter What is the f-number (f-stop) of the same lens when the diaphragm reduces the diameter of the lens from 10 mm to 5 mm? 10 5 40 mm focallength lens at full apertureof diameter d = 10 mm 40 mm focallength lens with apertureof diameterd = 5 mm What are apertures, f-numbers and stops? 40 f = 4 ( = f/4) f-number =  10 d a) f/2, b) f/4, c) f/6, d) f/8, e) f/10

22. Exam # 1 was & extra credit assignments • A. Trivial • B. Relatively easy; • C. Appropriate; • D. Difficult; • E. Overwhelmingly difficult; • A. I will do extra credit projects to improve my grade (20points/project); • B. I will not do extra credit projects;

29. single lens reflex (SLR) is most folks' idea of a serious camera. SLR means that the same lens is used for viewing and taking pictures. A mirror in the body directs the light from the lens up into a prism for viewing, then flips up out of the way just before an exposure is made. These are extremely versatile instruments in the right hands and can take beautiful pictures if used with care.

30.  is the symbol which means proportional to A  d2 means A = const·d2 If d is doubled A increases by a factor of 4 no matter what the constant is!! Example A = 0.785 d2 If d = 2.5, then A = 0.785·2.5·2.5 = 4.91 But if d is doubled from 2.5 to 5, then A = 0.785·5·5= 19.64 which is 4 times 4.91 It is even easier to use proportionality since the constant doesn't matter: A  d2 Double d by multiplying by 2 Note (2d)2 = 4d2 so the new area is 4 times the old area. Mini-lesson on proportionality

31. The volume, V, of a spherical balloon is proportional to its diameter, d, cubed: V d3 If the diameter is doubled by how much does the volume change? a factor 2 a factor 4 a factor 6 a factor 8 Answer: (2d)3 = 23·d3 = 8·d3, so the answer is a factor of 2 The diameter of a circle is proportional to the square root of its area d √A If the area is made 4 times larger, by what factor is the diameter increased? b) √2, c) 4 Ans: √(4A) = √4·√A = 2·√A Practice questions

32. A larger aperture lens brings more rays from each point on the object to the corresponding point on the image Consider Alex's image A pinhole only lets one ray from his nose converge at the image nose. Image is dim (not intense) A small aperture lens makes more rays from his nose converge to the image nose. Image is brighter (more intense) A large aperture lens allows still more rays from his nose to converge to the image nose. Image is still brighter (too intense) Why do we squint in bright light? A lens with a largeraperture lets more light energy reach each point on the image at the back of a camera (where film or a CCD lies) Pinhole Small aperture lens Large aperture lens with samefocal length as smaller aperture lens

34. Light energy  Lens area Area, A, of lens is proportional to lens diameter, d, squared A  d2 Therefore, lens diameter, d, is proportional to square root of lens area d  √A Double the area and d increases by what factor? √2 2 4 Lens d diameter of lens = d Light energy reaching film each second is proportional totheAREA of lens Camera Area of lens = A = π(d/2)2

35. f-stop = (focal length)/d The f-stop at right has diameter d = 5 and f-stop 40/5 = 8 Suppose we double thediameter, d The new f-stop is 40/2d = 4 The new area of the aperture is proportional to the square of the new diameter: A d)2 = 4d2, an increase by a factor of 4 This lets in 4 times the amount of light energy (since energy  Area) How can we just double the energy reaching the film? Multiply diameter, d, by number √2 The area (√2d)2 = √22d2 is doubled because √22 = 2 The f-stop (√2d) is decreased by a factor of 1/√2 from f/8 to f/5.6 5 10 5·√2 40 mm focallength lens with apertureof diameterd = 5 mm 40 mm lens at full apertureof diameter 2d = 10 mm More light energy reaches the film when the f-stop of the lens is decreased new diameter= √2·d mm = 7.1 mm 40/(√2·d)= f/5.6 40/(2d)= f/4 40/d = f/8 Area = π ·(√2·d/2)2= 12.5 mm2(twice the light energyas at f/8) Area= π ·(d/2)2= 6.25 mm2 Area= π·(2d/2)2= 25 mm2(4 x the light energy as at f/8)

36. f/22 f/16 f/11 f/8 f/5.6 f/4 f/2.8 f/2 f/1.4 Smaller f-stops mean larger diameters, less depth of field, larger aperture areas and more light energy gets to film f-stop or f-number defined as= (focal length)/(diameter of lens) Each f-stop down the list has a diameter, d, larger by factor √2 than the previous stop has an aperture area (d2) larger by factor 2 Lets in twice the light energy (energy area) Sequence of f-stops which each let in twice the light energy per sec Smallerf-stops Depth of field video

37. You get more of a sunburn if the suns rays hit your skin longer Each second more light energy hits your skin Less light energy goes into your your eye if you open and close it again quickly More light arrives at the CCD at the back of a camera when the shutter is left open longer Image gets brighter if shutter is left open longer A light wave continues to deliver energy as long as the wave keeps moving into an eye or a lens

38. 1/15 sec 1/30 sec 1/60 sec 1/125 sec 1/250 sec 1/500 sec 1/1000 sec 1/2000 sec Sequence of shutter speeds in which each faster speed lets in half the light energy Faster speeds, better able tostop (freeze) fast motionbut give darker image

39. The exposure of film (or a CCD) is proportional to the total amount oflight energy falling on the film (or CCD) during the time the shutter is left open Sometimes the exposure is defined in terms of the intensityof light at the film YouTube Video on shutter and aperature The intensity of light on the film is defined as the energy delivered per second divided by the area of the film The exposure is proportional to the lightintensity × the time interval that the shutter is left open Hence the exposure depends on both the f-stop (which controls the intensity) and the shutter speed which is the time the shutter is left open What is meant by exposure of a picture?

40. f/22 f/16 f/11 f/8 f/5.6 f/4 f/2.8 f/2 f/1.4 Large depth of field because of small aperture, but slow shutter speed near top of list may give motion blur Fast shutter speed but small depth of field near bottom of list due to large apertures. but image may be out of focus due to small depth of field Twice the energy gets in each second Half the time for energy to get in Equivalent combinations of f/stops and shutter speeds (which deliver the same energy to the film or CCD). All give sameexposure! • 1/15 sec • 1/30 sec • 1/60 sec • 1/125 sec • 1/250 sec • 1/500 sec • 1/1000 sec • 1/2000 sec • 1/4000 sec

41. Intensity of light is defined as energy per second per unit area Power = energy per second (watts) How many watts is that light bulb in your room? Intensity = powerdivided byarea Power comning out from light bulb is same as we move away (say, 60 watts)but intensity decreases Alex sees intensity (power reaching his eye is intensity times his eye area) Intensity is proportional to 1/r2 r is the distance from the center of the light bulb to your eye Intensity therefore falls off as the square of the distance Think of how dim a star seems!! Why can't your camera flash sometimes supply enough light? r Light is more intense when there is more energy per unit area. Light bulb Draw an imaginary sphere whose radius, r is thedistance from your eye to the center of the light bulb • The intensity of light is the same everywhere on the sphere and equal to the power divided by the area of the sphere The area of the sphere is proportional to r2 so the intensityis proportional to 1/r2

42. Intensity of light is energy per second per unit area Light is more intense when there is more energy per unit area How does the intensity change when the image is larger? Is the intensity of light on the film of the telephoto camera higher, b) lower, c) the same The same light energy is spread over a larger area so the intensity goes down To compensate for this lower intensity cameras we use a lens to let in more light than a pinhole can. How we can understand the concept of intensity in terms of the images from pinhole cameras.

43. Why is f-number = f/d? Consider a lens with a different focal length but the samef-number: It must have a larger diameter for a larger focal lengths (by definition) The larger diameter lens brings more rays to each image point so that the same light intensity arrives at the film (for same source) If the lens were not larger the image would be less intense (dimmer), as in the pinhole camera So the definition guarantees that every f/2 lens gives the same exposure for the same shutter speed, regardless of whether it's focal length is small or large (wide-angle or telephoto). 20 mm f = 40 mm 30 mm fnew = 60 mm Why is the f-number defined as the focal length divided by the lens aperture diameter? f/2 lens with focal length 40 mm means2= 40/d, so lens has diameter d = 20 mm f/2 lens with focal length 60 mm means2= 60/d, so lens has diameter d = 30 mm

44. If the 60 mm lens did not have a larger diameter than the 40 mm lens, the intensity of the larger image would be smaller by 1/xi2, where xi is the distance to Alex's image But if Alex is far enough in front of the lens (a few feet) we found that xi is approximately the same as the focal length, f Hence, the image intensity would decrease as 1/f2 To compensate, the larger lens diameter (d) lets in more intensity by the factor d2 (area) The ratio d2/f2 = 1/(f-number)2 so that if both lenses have the same f-number there is no change in intensity We can prove that two lenses with the same f-number give an image of Alex with the same light intensity 20 mm f = 40 mm f/2 lens with focal length 40 mmmust have diameter 20 mm f/2 lens with focal length 60 mmmust have diameter 30 mm 30 mm fnew = 60 mm

45. As the distance between the pinhole and the back of the pinhole camera is increased the image increases in size The first camera gives a wide-angle effect because the film is covered by an image that includes more than Alex The longer camera gives a telephoto effect because Alex's image covers the entire film the angle between the crossed yellow lines is smaller in the longer camera with the larger image! The image stays in focus (sharp) Wide angle and telephoto lenses work the same way That's why telephoto lenses are long They often have large diameters, to let in as much light as a normal lens would Film covers back of camera smallerangle Wide angle and telephoto effects in the pinhole camera only depend on the distance from pinhole to film

48. For photography of objects at different distances from us we use • A. Camera with CCD that has at least 5 megapixels; • B. Small aperture (large f-number); • C. Large aperture (small f-number); • D. Short exposure; • E. A, B, C, & D

49. For photography of moving objects we use • A. Camera with CCD that has at least 5 megapixels; • B. Small aperture (large f-number); • C. Large aperture (small f-number); • D. Short exposure and larger aperture; • E. A, B, C, & D

50. Extra credit questions • What settings we use for small depth of field? • What settings we use to make photos late in the evening (not much light)? • What would you do to make a photo during a very sunny day? • Explain how the photo on the left was done