Physics 102: Lecture 19 Lenses and your EYE Ciliary Muscles

Transcription

1 Physics 02: Lecture 9 Lenses and your EYE Ciliary Muscles Physics 02: Lecture 9, Slide

2 3 Cases for Converging Lenses Object Past 2F Image Inverted Reduced Real Object Between F & 2F Image Inverted Enlarged Real Image Object Inside F Upright Enlarged Virtual Physics 02: Lecture 9, Slide 2

3 Only Case for Diverging Lenses Object F Image F P.A. Image is always virtual, upright, and reduced. Physics 02: Lecture 9, Slide 3

4 Preflight 9. A converging lens is used to project a real image onto a screen. A piece of black tape is then placed over the upper half of the lens. Physics 02: Lecture 9, Slide 4

5 Lens Equation Same as mirror equation d o + d i = f Object d o F f F P.A. Image d o = distance object is from lens: Positive: object in front of lens Negative: object behind lens d i = distance image is from lens: Positive: real image (behind lens) Negative: virtual image (in front of lens) f = focal length lens: Positive: converging lens Negative: diverging lens Physics 02: Lecture 9, Slide 5 5 cm m + d i d i d i = 0 cm = 30 cm d d i = = 2 o

6 Multiple Lenses Image from lens becomes object for lens 2 2 f f 2 Lens creates a real, inverted and enlarged image of the object. Lens 2 creates a real, inverted and reduced image of the image from lens. The combination gives a real, upright, enlarged image of the object. Physics 02: Lecture 9, Slide 6

7 Multiple Lenses: Image d o = 5 cm 2 f = 0 cm f f 2 d i = 30 cm f 2 = 5 cm First find image from lens. 5 cm + d i = 0 cm d i = 30 cm Physics 02: Lecture 9, Slide 7

8 Multiple Lenses: Image 2 d o = 5 cm 2 L = 42 cm d i = 8.6 cm f = 0 cm f f 2 d i = 30 cm f 2 = 5 cm d o =2 cm Now find image from lens 2. 2 cm + Physics 02: Lecture 9, Slide 8 d i = 5 cm d i = 8.6 cm Notice that d o could be negative for second lens!

9 Multiple Lenses: Magnification d o = 5 cm 2 L = 42 cm d i = 8.6 cm f = 0 cm f f 2 d i = 30 cm f 2 = 5 cm d o =2 cm Net magnification: m net = m m m = = 2 m2 = = Physics 02: Lecture 9, Slide 9 m net = m m 2 = +.43

10 The Eye One of first organs to develop. ~00 million Receptors ~200,000 /mm 2 Sensitive to single photon! Candle from 2 miles Ciliary Muscles Physics 02: Lecture 9, Slide 0

11 ACT: Focusing and the Eye Cornea n=.38 Lens n =.4 Vitreous n =.33 Ciliary Muscles Which part of the eye does most of the light bending? ) Lens 2) Cornea 3) Retina 4) Cones Physics 02: Lecture 9, Slide

12 Eye (Relaxed) 25 mm Determine the focal length of your eye when looking at an object far away. Object is far away: d o = + 25 mm = f Want image at retina: d i = 25mm f relaxed = 25 mm Physics 02: Lecture 9, Slide 2

13 Eye (Tensed) 250 mm 25 mm Determine the focal length of your eye when looking at an object up close (25 cm). Object is up close: Want image at retina: Physics 02: Lecture 9, Slide 3 d o = 25 cm = 250mm d i = 25mm 250 mm f tense f relaxed + 25 mm = = 22.7 mm = 25 mm f

14 Near Point, Far Point Eye s lens changes shape (changes f ) Object at any d o should have image be at retina (d i = approx. 25 mm) Can only change shape so much Near Point Closest d o where image can be at retina Normally, ~25 cm (if far-sighted then further) Far Point Furthest d o where image can be at retina Normally, infinity (if near-sighted then closer) Physics 02: Lecture 9, Slide 4

15 Preflight 9.3 A person with normal vision (near point at 26 cm) is standing in front of a plane mirror. What is the closest distance to the mirror where the person can stand and still see himself in focus? ) 3 cm 2) 26 cm 3) 52 cm Physics 02: Lecture 9, Slide 5

16 If you are nearsighted... Too far for near-sighted eye to focus (far point is too close) d o d o + = d far f lens d far Near-sighted eye can focus on this! + d far = f lens Contacts form virtual image at far point becomes object for eye. Want to have (virtual) image of distant object, d o =, at the far point, d i = -d far. f lens = - d far Physics 02: Lecture 9, Slide 6

17 Refractive Power of Lens Diopter = /f where f is focal length of lens in meters. Example: My prescription reads -6.5 diopters f lens = -/6.5 = m = -5.4 cm (a diverging lens) d far = 5.4 cm (!) Physics 02: Lecture 9, Slide 7 f lens = - d far

18 If you are farsighted... (near point is too far) Too close for far-sighted eye to focus d near Far-sighted eye can focus on this! d o d o + = d near f lens Want the near point to be at d o. Contacts form virtual image at near point becomes object for eye. When object is at d o, lens must create an (virtual) image at -d near Physics 02: Lecture 9, Slide 8 25 cm f + 50 cm = 50 cm = f

19 Farsightedness + = do di flens Near point d near > 25 cm To correct, produce virtual image of object at d 0 = 25 cm to the near point (d i = d near ) + = d d f o near lens + = d f 25 near lens Example: My near prescription reads +2.5 diopters f lens = +/2.5 = 0.4 m = 40 cm therefore d near = 67 cm (with my far correction) Physics 02: Lecture 9, Slide 9

20 ACT/Preflight 9.4 Two people who wear glasses are camping. One of them is nearsighted and the other is farsighted. Which person s glasses will be useful in starting a fire with the sun s rays?. nearsighted 2. farsighted Physics 02: Lecture 9, Slide 20

21 Angular Size Preflight 9.6, 9.7 Both are same size, but nearer one looks bigger. θ θ θ θ Angular size tells you how large the image is on your retina, and how big it appears to be. How small of font can you read? Highwire Caramel Apples Rabbits Kindergarten Hello Arboretum Halloween Amazing Physics 02: Lecture 9, Slide 2

22 Angular size: Unaided Eye object How big the object looks with unaided eye. h 0 θ d near Bring object as close as possible (to near point d near ) tan( θ ) = h d o near θ h d o near ** If θ is small and expressed in radians. Physics 02: Lecture 9, Slide 22

23 Magnifying Glass virtual image magnifying glass h i / θ h o object Magnifying glass produces virtual image behind object, allowing you to bring object to a closer d o : and larger θ θ / = h i = h o h0 Compare to unaided eye: : d i d θ = o d Ratio of the two angles is the angular magnification M: θ ho do dnear M = = = θ h d d Physics 02: Lecture 9, Slide 23 d i near d o o near o

24 Angular Magnification virtual image object / h θ i h o do magnifying glass (d near = near point distance from eye.) h d d d i θ o o near M = = = For the lens : + = θ ho dnear do d o d i f For max. magnification, put image at d near : d o = f d i M = d near /d 0 = d near /f + so set d i = -d near : = + d f d o near Smaller f means larger magnification Physics 02: Lecture 9, Slide 24

25 Summary Lenses Lens equation & magnification Multiple lenses The eye Near & far point Nearsightedness & farsightedness & corrective lenses Angular magnification Physics 02: Lecture 9, Slide 25