2. Coherent Interference Intensity

3. Huygens’ Principle Section 25.4

4. Double Slit Analysis Section 25.5 Constructive interference d sin θ = m λ Destructive interference d sin θ = (m + ½) λ

5. Single-Slit Analysis Destructive interference w sin θ = ±m λ Section 25.6

6. Diffraction Grating ΔL = d sin θ = m λ Section 25.7

7. Rayleigh Criterion Section 25.8

8. Applications of Optics Chapter 26

9. Applications of Optics Many devices are based on the principles of optics Eyeglasses around 1200s Perhaps the oldest optical instrument Microscopes and telescopes around 1600 CDs and DVDs around 1980s Also improvements to devices have been made

10. Applications of a Single Lens The eye can be modeled as a single lens with a focal length ƒ eye Eyeglasses and contact lenses add a lens in front of the eye A magnifying glass is also a single lens Section 26.1

11. Normal Eye Light emanating from a point on the object is focused to a corresponding point on the retina The near-point distance, s N, is the closest distance an object can be that you can focus (~25 cm) Objects nearer than the near-point cannot be focused on the retina Section 26.1

12. Normal Eye, cont. The normal eye can also focus on objects that are very far away s ~ ∞ The eye must adjust its focal length to values between s N and ∞ Does this by using muscles that deform and change the shape of the eye’s lens Needs to change from about 2.3 cm to 2.5 cm Section 26.1

13. Glasses and Contact Lenses Glasses or contact lenses are lenses placed in front of the eye Along with the eye, these form a system of lenses One lens from the eye and one from the glasses or contact Systems of lenses contain two or more lenses The same analysis idea will be applied to telescopes, microscopes and other optical instruments Section 26.1

14. Analysis for a System with Two or More Lenses Draw a picture showing the object of interest and the lenses in the problem Use the rules for ray tracing along with the thin-lens equations to find the location and magnification produced by the first lens in the system The image produced by the first lens then acts as the object of the second lens in the system Use the rules for ray tracing and the thin-lens equations a second time to find the location and magnification produced by the second lens in the system Section 26.1

15. Far-Sighted Vision The near-point distance is greater than for a normal eye Objects located closer than the near-point distance cannot be focused To compensate, a lens can be placed in front of the eye Section 26.1

16. Far-Sighted Correction The contact (or glasses) lens is the first lens in the system For example, if a person’s near-point distance is 75 cm, the corrective lens needs to be a converging lens with ƒ lens = 38 cm If the person’s near-point distance is greater than 75 cm, the focal length of the corrective lens needs to be shorter Section 26.1

17. Diopters The strength of a lens is sometimes measured in terms of its refractive power Units are m -1 which is called a diopter For example, the lens with ƒ = 38 cm will have a refractive power of 2.7 diopters Section 26.1

18. Near-Sighted Vision A nearsighted person is unable to focus light from distant objects on the retina The incoming rays from an object very far away are approximately parallel to the axis (at infinity) A nearsighted eye produces an image in front of the retina

19. Near-Sighted Correction The object at ∞ needs to focus on the retina For example, if the person can focus objects within 2.0 m, the corrective lens needs to be a diverging lens with ƒ lens = -2.0 m

20. Glasses The eyeglass lens is a short distance in front of the eye Instead of touching it as with the contact lens The distance must be taken into account This generally makes the focal length of the eyeglasses about 10% shorter than a contact lens Section 26.1

21. Magnifying Glass The simplest magnifying glass is a single lens Again it can be considered a system of two lenses The magnifying lens and the eye The goal is to produce a greatly magnified image at the retina Want the image on the retina to be as large as possible Analysis is similar to that for contact lenses or eyeglasses Section 26.1

22. Magnifying Glass, cont. The largest clearly focused image for the unaided eye results when the object is at the near point The object’s apparent size when it is located at the near point can be measured using the angle θ Section 26.1

23. Image Properties with a Magnifying Glass The object is positioned inside the focal length of this lens This position of the lens produces an upright virtual image at a point farther from the eye The eye perceives the light as emanating from this virtual image The image angle with the magnifying glass is greater than the image angle for the eye alone The image on the retina is enlarged by the magnifying glass Section 26.1

24. Angular Magnification The enlargement of the image on the retina is given by the angular magnification m θ From geometry and the small angle approximations, The angular magnification of a typical magnifying glass is usually 10 or 20 Section 26.1

25. Microscopes Lenses with focal lengths less than a few mm are difficult to make There is a practical limit to the magnification of a single lens A more useful way to achieve higher magnification is using two lenses arranged as a compound microscope The image produced by one lens is used as the object of the second lens The image produced by the second lens is then viewed by the eye The total magnification is the product of the magnifications of the two lenses Section 26.2

26. Compound Microscope The two lenses are called the objective and the eyepiece To analyze the image produced first apply ray tracing and the thin-lens equation to find the image produced by the objective lens This image acts as the object for the eyepiece The image produced by the eyepiece is viewed by the eye Section 26.2

27. Compound Microscope, cont. The distance between the objective lens and the original object is adjusted so that the image produced by the objective falls at the focal point of the eyepiece This gives a final virtual image for the observer The linear magnification of the objective lens is Section 26.2

28. Compound Microscope, Magnification The total magnification of the microscope is the product of the linear magnification of the objective and the angular magnification of the eyepiece The negative sign indicates that the image is inverted Section 26.2

29. Advances in Microscope Design The index of refraction of the glass used to make the lenses is slightly different for light of different colors This makes the focal length slightly different for different colors This affects the focusing properties of a microscope Called chromatic aberration Chromatic aberration can be corrected by using an achromatic lens This is a lens composed of different types of glass with different indices of refraction which approximately cancels the aberrations Section 26.2

30. Resolution of a Microscope There is a fundamental limit to the resolution that can be achieved with any microscope that relies on focusing This limit is due to the diffraction of light passing through the aperture of the microscope Diffraction prevents the size of the focused spot from being less than a value approximately equal to the wavelength of the light Section 26.2

31. Resolution, cont. It is possible to resolve the outgoing light from two features only if they are separated by a distance approximately equal to the wavelength of the light that is used If they are closer, it is not possible to tell that there are two separate features Section 26.2

32. Resolution, final Optical resolution is set by diffraction It is approximately equal to the wavelength of the light used Applications requiring the best possible resolution use blue or ultraviolet light These color have the shortest wavelength compared with other colors of visible light Section 26.2

33. Confocal Microscope A confocal microscope is designed so that features at only one particular depth form the final image This is done by placing a pinhole in front of the observer The depth of resolution is again limited by diffraction effects Depths must be greater than λ to be separated Section 26.2

34. Telescopes When using a telescope, the light rays from the object are nearly parallel The object is approximately at infinity One purpose of a telescope is to increase the angular separation between two stars This allows your eye to distinguish one star from the other Section 26.3

35. Refracting Telescope A refracting telescope use lenses Objective lens and eyepiece Was invented around 1600 and was the type used by Galileo The objective lens forms an image of the object This image then acts as the object for the second lens Section 26.3

36. Refracting Telescope – Image For the objective lens The object is at infinity (approximately) The image forms at the focal point of the lens Eyepiece The eyepiece is located such that the image formed by the objective is very close to the focal point of the eyepiece The rays from the first image form a bundle of nearly parallel rays that are perceived by the observer Section 26.3

37. Refracting Telescope – Magnification The magnification is determined by the angles the incident ray (θ) and ray refracted by the eyepiece (θ T ) make with the axis Actually, this is the angular magnification From geometry and the small angle approximation Section 26.3

38. Reflecting Telescope – Newtonian Design Newton designed a reflecting telescope Uses mirrors Advantages The mirrors will not have any chromatic aberration Easier to make a high- quality mirror than a lens For a given diameter, a mirror is lighter and easier to support Section 26.3

39. Reflecting Telescope – Cassegrain Design In the Cassegrain design, light reflects from the primary mirror, then from a secondary mirror and travels through a small hole in the primary mirror The light then travels through an eyepiece to the observer The Hubble Space Telescope is an example of a Cassegrain design Section 26.3

40. Magnification – Reflecting Telescope The concave mirror forms a real image of a distant object very close to the focal point of the mirror A second mirror is positioned in front of the focal point and reflects the light to an eyepiece The magnification is similar to that for the refracting telescope, with ƒ M being the focal length of the primary mirror Section 26.3

41. Resolution of a Telescope Resolution determines how close together in angle two stars can be and yet still be seen as two separate stars The resolution is limited by two factors Diffraction at the telescope’s aperture Atmospheric turbulence The aperture is generally the same diameter as the primary mirror From the Rayleigh criterion, the limiting angular resolution set by diffraction is Section 26.3

42. Resolution, cont. Most telescopes do not attain the resolution limit Starlight must pass through many kilometers of air before reaching an observer on Earth The turbulent motion of the air causes fluctuations in the refractive index from place to place The fluctuations act like lenses and refract the incoming light from the star The “lenses” are constantly changing, so the direction of the starlight changes as well This makes the star “twinkle” Section 26.3

43. Atmospheric Effects For a location on the Earth’s surface, the angular spread caused by atmospheric turbulence is typically 1" (one arc second) 1° = 60 arc minutes 1 arc minute (1') = 60 arc seconds The value for this angular spread is smaller at higher altitudes Telescopes in space eliminate atmospheric effects and the resolution is determined by the diffraction limit of the primary mirror Section 26.3

44. Adaptive Optics The technology of building telescopes with adjustable mirrors to compensate for atmospheric distortion is called adaptive optics A reference star is an object known to appear as a point source As the atmosphere causes the image of the reference star to be smeared out, the telescope’s mirror is adjusted to make the image as perfect as possible Computers allow for rapid and accurate control of the mirror shape Section 26.3

45. Cameras Cameras are common optical devices A simple camera consists of a single lens positioned in front of a light-sensitive material The lens forms an image on the detector An aperture is opened for a short time to allow sufficient light energy to enter Section 26.4

46. Film Camera The distance between the camera’s lens and the film determines which objects are in focus The standard lens for a 35 mm camera is 40 mm The “35 mm” is from the size of the film 24 mm x 35 mm Section 26.4

47. Film Camera, cont. Other lenses can be purchased with different focal lengths Since the object is far away from the camera, a good approximation is that the image forms at the focal point The linear magnification of the image is The image is real and inverted Section 26.4

48. Digital Camera A digital camera replaces film with a CCD A CCD is a charge-coupled device A CCD uses a type of capacitor to detect light and record its intensity The optical system of a digital camera is basically the same as that of a film camera There are important differences Section 26.4

49. CCD A CCD is fabricated in an integrated circuit chip The chip contains many capacitors arranged in a grid When light strikes the chip, it is absorbed in the dielectric layer and ejects some electrons from their normal chemical bonds Section 26.4

50. CCD, cont. The ejected electrons move to the capacitor plate This leads to a voltage across the capacitor that is closest to where the light was absorbed This voltage is detected by additional circuitry and its value is stored in a computer memory in the camera The magnitude of the voltage depends on the light intensity The greater the intensity, the higher the voltage The pattern of voltages on the capacitors gives the light intensity as a function of position Section 26.4

51. CCD, final One way to measure the color is to combine the information from four adjacent capacitors Filters allow different colors to pass through to the capacitor The camera’s computer can estimate the average color over the region Section 26.4

52. Pixels Each region forms a pixel From picture element The image produced by the CCD is stored by the camera as a set of intensity and color values for each pixel An important specification is the number of pixels in each photograph A larger number of pixels indicates a finer level of detail in the photograph Section 26.4

53. Optics of a Digital Camera The size of the CCD is much smaller than the area of the film Typically about 6 mm x 8 mm The magnification is still Since the detector is smaller, the image height must be smaller The focal length must be smaller for a digital camera About 4 times smaller Section 26.4

54. Optics, cont. The lens in the digital camera must be closer to the detector The distance between the lens and the CCD is approximately the focal length of the lens This allows the digital camera to be much thinner than a film camera The optical zoom function changes the magnification of a digital camera by moving the lens relative to the CCD detector A digital zoom process constructs the entire photo using just the image data from near the center of the CCD grid This uses fewer pixels and has poorer resolution than without the digital zoom Section 26.4

55. ƒ-Number Settings for both film and digital cameras include shutter speed and the ƒ-number Shutter speed is the amount of time the film or CCD is exposed to light from the object The ƒ-number is associated with the camera’s aperture The aperture is an opening that controls the open area of the lens Section 26.4

56. ƒ-Number, cont. The ƒ-number is the ratio of the focal length to the aperture diameter A large aperture gives a small ƒ-number This allows more light to reach the film or the CCD

57. Shutter Speed and ƒ-Number There is a trade-off between shutter speed and ƒ-number If you reduce shutter speed, you need to compensate by increasing the ƒ-number Same Exposure Value (Camera settings) can have different f-number and time Halving f-number reduces EV by sqrt(2) Section 26.4

58. Depth of Focus and ƒ-Number With a small aperture (large ƒ-number) the blurring of images away from the best focus is small With a large aperture (small ƒ-number) some rays make a large angle with the central ray They diverge more quickly as one moves away from the image point The ƒ-number is also related to the depth of focus Having a large depth of focus means that objects that are not at the best focusing point will produce images that are still close to ideal Section 26.4

59. Pinhole Camera The pinhole camera makes the aperture very tiny No lens is needed A sharp image can result The intensity is very low and so you need long exposure times Allows safe viewing of intense light sources such as the Sun Section 26.4

60. CD CDs and DVDs are applications of optics that can only be understood in terms of the ideas of wave optics CDs and DVDs operate through similar principles Structure is a plastic layer that is smooth on the bottom and contains a pattern of pits on the top Section 26.5

61. CD Structure The pattern of pits on the top surface is used to encode information on the CD The top surface is coated with a thin layer of aluminum to make it reflecting It is then covered with a protective layer of lacquer The label is placed over the lacquer The pits are arranged in a long spiral track Information encoded in the pits is read by reflecting a laser beam from the aluminum surface Laser light passes in and out through the bottom surface of the plastic, so the surface must be kept clean Section 26.5

62. Reading a CD The layer of aluminum acts as a mirror It reflects the laser light The pits influence this reflection through thin- film interference effects The pit depth is designed to produce destructive interference

63. Reading a CD, cont. There is no reflected light when the laser beam is over a pit edge The intensity is large when the laser beam is over the center of a pit or is outside a pit As the laser beam travels along a track, the reflected light intensity varies between zero and a large value These high and low values of the intensity correspond to ones and zeros in a binary encoding of information on the CD Section 26.5

64. Reading a CD, final To store as much information as possible on the CD, the pits must be as small as possible The minimum size is approximately equal to the wavelength The limit is set by wave optics Differences in DVDs Shorter wavelength lasers allow pits to be closer together Multiple layers of aluminum Pits probed on both sides Section 26.5

65. Optical Fibers Optical fibers are flexible strands of glass that conduct and transmit light by using total internal reflection Remember whenever the angle of incidence is greater than the critical angle, all the light is reflected at the surface Section 26.6

66. Optical Fiber Design The central cos is surrounded by an outer layer called the cladding The core and cladding are both made of glass Different compositions and different indices of refraction With n cladding < n core, total internal reflection of the light in the core can occur Modern fibers have smaller core diameters that require wave optics to analyze Section 26.6

67. NSOM The wavelength of light sets a limit on the resolution of a compound microscope Light cannot be focused to a spot size smaller than its wavelength Details smaller than λ can be perceived using near- field scanning optical microscopy (NSOM) Section 26.7

68. NSOM, cont. The technique uses an optical fiber to illuminate a very tiny region at the end of the fiber The light is most intense at the opening of the tip This can be much smaller than the wavelength The tip is positioned very close to the object to be studied It is then scanned over one of its surfaces Because the tip is so close to the object, only a very small area near the tip is strongly illuminated Resolution is then determined by the spacing from the surface and the tip diameter Both can be much smaller than the wavelength Section 26.7

69. NSOM, final By measuring the scattered or reflected light, an image of the surface can be constructed Based on the scattered intensity as a function of the tip’s position Current NSOM fibers have openings much smaller than visible light wavelengths About 45 nm openings The technique is being used to create images of objects as small as individual molecules Section 26.7