Review!

1. Review!

2. Coherent Interference Intensity

3. Huygens’ Principle Section 25.4

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

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. Chapter 26 Applications of Optics

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 ƒeye • 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-pointdistance, sN, 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 sN 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 ƒlens = 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 ƒlens = -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 mθ • 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 (θT) 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 ƒM 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