Optical Instruments - The Camera

1. Chapter 25 Chapter 25 Optical Instruments Optical Instruments Conceptual questions: 3,6,7,8,9 Quick quiz: 2 Problem: 10,26,48

2. The Camera The Camera The ƒ-number of a camera is the ratio of the focal length of the lens to its diameter The ƒ-number of a camera is the ratio of the focal length of the lens to its diameter ƒ = f/D ƒ = f/D The ƒ-number is often given as a description of the lens “speed” The ƒ-number is often given as a description of the lens “speed” The lowest ƒ-number setting on a camera corresponds to the aperture wide open and the maximum possible lens area in use The lowest ƒ-number setting on a camera corresponds to the aperture wide open and the maximum possible lens area in use M=h’/h=-q/p h’=-hf/p Camera with small f produces small images

3. The Eye The Eye Essential parts of the eye Essential parts of the eye Cornea – light passes through this transparent structure Cornea – light passes through this transparent structure Aqueous Humor – clear liquid behind the cornea Aqueous Humor – clear liquid behind the cornea The pupil The pupil A variable aperture A variable aperture An opening in the iris An opening in the iris The crystalline lens The crystalline lens The retina The retina The retina contains receptors called rods and cones The retina contains receptors called rods and cones

4. Iris Iris The iris is the colored portion of the eye The iris is the colored portion of the eye It is a muscular diaphragm that controls pupil size It is a muscular diaphragm that controls pupil size The iris regulates the amount of light entering the eye by dilating the pupil in low light conditions and contracting the pupil in high-light conditions The iris regulates the amount of light entering the eye by dilating the pupil in low light conditions and contracting the pupil in high-light conditions The f-number of the eye is from about 2.8 to 16 The f-number of the eye is from about 2.8 to 16

5. The Eye – Operation The Eye – Operation Rods and Cones Rods and Cones Chemically adjust their sensitivity according to the prevailing light conditions Chemically adjust their sensitivity according to the prevailing light conditions The adjustment takes about 15 minutes The adjustment takes about 15 minutes This phenomena is “getting used to the dark” This phenomena is “getting used to the dark” Accommodation Accommodation The eye focuses on an object by varying the shape of the crystalline lens through this process The eye focuses on an object by varying the shape of the crystalline lens through this process An important component is the ciliary muscle which is situated in a circle around the rim of the lens An important component is the ciliary muscle which is situated in a circle around the rim of the lens Thin filaments, called zonules , run from this muscle to the edge of the lens Thin filaments, called zonules , run from this muscle to the edge of the lens 1/f = 1/p +1/q for an eye q=1.7 cm

6. The Eye -- Focusing The Eye -- Focusing Lens maker’s formulae Lens equation the ciliary muscle is relaxed and the zonules tighten, as a result When the eye focuses on a distant object, the ciliary muscle is relaxed and the zonules tighten, as a result the lens flattens, R 1 and R 2 increase. When the eye focuses on near objects, the ciliary muscles tenses, this relaxes the zonules, and the lens bulges a bit and the focal length decreases. The image is focused on the retina. When the eye focuses on near objects, the ciliary muscles tenses, this relaxes the zonules, and the lens bulges a bit and the focal length decreases. The image is focused on the retina.

7. The Eye – Near and Far Points The Eye – Near and Far Points The near point is the closest distance for which the lens can accommodate to focus light on the retina The near point is the closest distance for which the lens can accommodate to focus light on the retina Typically at age 10, this is about 18 cm Typically at age 10, this is about 18 cm It increases with age It increases with age The far point of the eye represents the largest distance for which the lens of the relaxed eye can focus light on the retina The far point of the eye represents the largest distance for which the lens of the relaxed eye can focus light on the retina Normal vision has a far point of infinity Normal vision has a far point of infinity

8. Farsightedness Farsightedness Also called hyperopia The image focuses behind the retina Can usually see far away objects clearly, but not nearby objects

9. Correcting Farsightedness Correcting Farsightedness A converging lens placed in front of the eye can correct the condition The lens refracts the incoming rays more toward the principle axis before entering the eye This allows the rays to converge and focus on the retina

10. Nearsightedness Nearsightedness Also called myopia In axial myopia the nearsightedness is caused by the lens being too far from the retina In refractive myopia , the lens-cornea system is too powerful for the normal length of the eye

11. Correcting Nearsightedness Correcting Nearsightedness A diverging lens can be used to correct the condition The lens refracts the rays away from the principle axis before they enter the eye This allows the rays to focus on the retina

12. Diopters Diopters The power of a lens in diopters equals the inverse of the focal length in meters The power of a lens in diopters equals the inverse of the focal length in meters P = 1/ƒ P = 1/ƒ

13. Problem 10. Problem 10. A PERSON HAS THE FAR POINT 84.4 CM FROM THE RIGHT EYE AND 122 CM FROM THE LEFT EYE. FIND THE POWERS FOR THE CORRECTIVE LENSES. A PERSON HAS THE FAR POINT 84.4 CM FROM THE RIGHT EYE AND 122 CM FROM THE LEFT EYE. FIND THE POWERS FOR THE CORRECTIVE LENSES.

14. The Size of a Magnified Image The Size of a Magnified Image Angular magnification Angular magnification is defined as is defined as

15. Magnification by a Lens Magnification by a Lens With a single lens, it is possible to achieve angular magnification up to about 4 without serious aberrations With a single lens, it is possible to achieve angular magnification up to about 4 without serious aberrations With multiple lens, magnifications of up to about 20 can be achieved With multiple lens, magnifications of up to about 20 can be achieved The multiple lens can correct for aberrations The multiple lens can correct for aberrations

16. Compound Microscope Compound Microscope The image formed by the first lens becomes the object for the second lens The image formed by the first lens becomes the object for the second lens The image seen by the eye, I 2 , is virtual, inverted and very much enlarged The image seen by the eye, I 2 , is virtual, inverted and very much enlarged

17. Magnifications of the Compound Microscope Magnifications of the Compound Microscope The lateral magnification of the objective is The lateral magnification of the objective is – L is the distance between the lenses – L is the distance between the lenses The angular magnification of the eyepiece of the microscope is The angular magnification of the eyepiece of the microscope is The overall magnification of the microscope is the product of the individual magnifications The overall magnification of the microscope is the product of the individual magnifications

18. Telescopes Telescopes Two fundamental types of telescopes Two fundamental types of telescopes Refracting telescope uses a combination of lens to form an image Refracting telescope uses a combination of lens to form an image Reflecting telescope uses a curved mirror and a lens to form an image Reflecting telescope uses a curved mirror and a lens to form an image Telescopes can be analyzed by considering them to be two optical elements in a row Telescopes can be analyzed by considering them to be two optical elements in a row The image of the first element becomes the object of the second element The image of the first element becomes the object of the second element

19. Refracting Telescope Refracting Telescope The two lenses are arranged so that the objective forms a real, inverted image of a distance object The two lenses are arranged so that the objective forms a real, inverted image of a distance object The image is near the focal point of the eyepiece The image is near the focal point of the eyepiece The two lenses are separated by the distance ƒ o + ƒ e which corresponds to the length of the tube The two lenses are separated by the distance ƒ o + ƒ e which corresponds to the length of the tube The eyepiece forms an enlarged, inverted image of the first image The eyepiece forms an enlarged, inverted image of the first image

20. Angular Magnification of a Telescope Angular Magnification of a Telescope The angular magnification depends on the focal lengths of the objective and eyepiece The angular magnification depends on the focal lengths of the objective and eyepiece The limiting angle of resolution depends on the diameter, D, of the aperture The limiting angle of resolution depends on the diameter, D, of the aperture

21. Reflecting Telescope, Newtonian Focus Reflecting Telescope, Newtonian Focus The incoming rays are reflected from the mirror and converge toward point A The incoming rays are reflected from the mirror and converge toward point A At A, a photographic plate or other detector could be placed At A, a photographic plate or other detector could be placed A small flat mirror, M, reflects the light toward an opening in the side and passes into an eyepiece A small flat mirror, M, reflects the light toward an opening in the side and passes into an eyepiece

22. Examples of Telescopes Examples of Telescopes Reflecting Telescopes Reflecting Telescopes Largest in the world are 10 m diameter Keck telescopes on Mauna Kea in Hawaii Largest in the world are 10 m diameter Keck telescopes on Mauna Kea in Hawaii Largest single mirror in US is 5 m diameter on Mount Palomar in California Largest single mirror in US is 5 m diameter on Mount Palomar in California Refracting Telescopes Refracting Telescopes Largest in the world is Yerkes Observatory in Wisconsin Largest in the world is Yerkes Observatory in Wisconsin Has a 1 m diameter Has a 1 m diameter

23. The diffraction pattern of a circular aperture consists of a central, circular bright region surrounded by progressively fainter rings The diffraction pattern of a circular aperture consists of a central, circular bright region surrounded by progressively fainter rings The limiting angle of resolution depends on the diameter, D, of the aperture The limiting angle of resolution depends on the diameter, D, of the aperture Resolution with Circular Apertures Resolution with Circular Apertures

24. Resolution Resolution For the images to be resolved, the angle subtended by the two sources at the slit must greater than θ min For the images to be resolved, the angle subtended by the two sources at the slit must greater than θ min

25. Suppose you are observing a binary star with a telescope and are having difficulty resolving the two stars. You decide to use a colored filter to help you. Should you choose a blue filter or a red filter? QUICK QUIZ 25.2

26. Michelson Interferometer Michelson Interferometer One ray is reflected to M 1 and the other transmitted to M 2 One ray is reflected to M 1 and the other transmitted to M 2 After reflecting, the rays combine to form an interference pattern After reflecting, the rays combine to form an interference pattern The glass plate ensures both rays travel the same distance through glass The glass plate ensures both rays travel the same distance through glass

27. Measurements with a Michelson Interferometer Measurements with a Michelson Interferometer The interference pattern for the two rays is determined by the difference in their path lengths The interference pattern for the two rays is determined by the difference in their path lengths When M 1 is moved a distance of λ/4, successive light and dark fringes are formed When M 1 is moved a distance of λ/4, successive light and dark fringes are formed This change in a fringe from light to dark is called fringe shift This change in a fringe from light to dark is called fringe shift The wavelength can be measured by counting the number of fringe shifts for a measured displacement of M The wavelength can be measured by counting the number of fringe shifts for a measured displacement of M If the wavelength is accurately known, the mirror displacement can be determined to within a fraction of the wavelength If the wavelength is accurately known, the mirror displacement can be determined to within a fraction of the wavelength

28. Conceptual questions Conceptual questions 6. Compare and contrast the eye and a camera. What parts of the camera correspond to the iris, the retina, and the cornea of the eye ? 6. Compare and contrast the eye and a camera. What parts of the camera correspond to the iris, the retina, and the cornea of the eye ? 3. The optic nerve and the brain invert the image formed on the retina. Why do we not see everything upside down? 3. The optic nerve and the brain invert the image formed on the retina. Why do we not see everything upside down? 8. If you want to use a converging lens to set fire to a piece of paper, why should the light source be farther from the lens than its focal point? 8. If you want to use a converging lens to set fire to a piece of paper, why should the light source be farther from the lens than its focal point? 7. Large telescopes are usually reflecting rather than refracting. List some reasons for this choice. 7. Large telescopes are usually reflecting rather than refracting. List some reasons for this choice. 9. Explain why it is theoretically impossible to see an object as small as an atom regardless of the quality of the light microscope being used. 9. Explain why it is theoretically impossible to see an object as small as an atom regardless of the quality of the light microscope being used.

29. Problem 25.26 Problem 25.26 A certain telescope has an objective of focal length 1 500 cm. If the Moon is used as an object, a 1.0 cm long image formed by the objective corresponds to what distance, in miles, on the Moon? Assume 3.8 × 10 8 m for the Earth–Moon distance.

30. Problem 25-48 Problem 25-48 A person with a nearsighted eye has near and far points of 16 cm and 25 cm, respectively. (a) Assuming a lens is placed 2.0 cm from the eye, what power must the lens have to correct this condition? (b) Suppose that contact lenses placed directly on the cornea are used to correct the person’s eye. What is the power of the lens required in this case, and what is the new near point? [ Hint: The contact lens and the eyeglass lens require slightly different powers because they are at different distances from the eye.] A person with a nearsighted eye has near and far points of 16 cm and 25 cm, respectively. (a) Assuming a lens is placed 2.0 cm from the eye, what power must the lens have to correct this condition? (b) Suppose that contact lenses placed directly on the cornea are used to correct the person’s eye. What is the power of the lens required in this case, and what is the new near point? [ Hint: The contact lens and the eyeglass lens require slightly different powers because they are at different distances from the eye.]