Today’s Lecture will cover textbook sections 23.9,24.1,3-4,6 Physics 102: Lecture 19 Lenses and your EYE Ciliary Muscles

40 3 Cases for Converging Lenses ImageObject Upright Enlarged Virtual Inside F Image Object Inverted Enlarged Real Between F & 2F Object Image Inverted Reduced Real Past 2F

1) Rays parallel to principal axis pass through focal point. 2) Rays through center of lens are not refracted. 3) Rays toward F emerge parallel to principal axis. Diverging Lens Principal Rays F F Object P.A. Only 1 case for diverging lens: Image is always virtual, upright, and reduced. 45 Image

Review of Lenses Preflight 18.8 P.A. F 5 Focal point determined by geometry and Snell’s Law: n 1 sin(   ) = n 2 sin(   ) Fat in middle = Converging Thin in middle = Diverging Larger n 2 /n 1 = more bending, shorter focal length. n 1 = n 2 => No Bending, f = infinity Lens in water has larger focal length! n 1 <n 2

Preflight 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.

Java 8 Preflight 19.1 Still see entire image (but dimmer)! (48% got correct) “There are still rays from the image bouncing off the lower half of the lens that will project the image. ”

Lens Equation 11 F F Object P.A. dodo didi f 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

Lens Equation 11 F F Object P.A. dodo didi f Image

Multiple Lenses Image from lens 1 becomes object for lens 2 1 f1f1 f2f2 2 Lens 1 creates a real, inverted and enlarged image of the object. Lens 2 creates a real, inverted and reduced image of the image from lens 1. The combination gives a real, upright, enlarged image of the object. 32

f1f1 f2f2 First find image from lens 1. d o = 15 cm f 1 = 10 cm d i = 30 cm f 2 = 5 cm Multiple Lenses: Magnification

f1f1 f2f2 Now find image from lens 2. d o = 15 cm f 1 = 10 cm d i = 30 cm f 2 = 5 cm L = 42 cm d o =12 cm d i = 8.6 cm Notice that d o could be negative for second lens! Multiple Lenses: Magnification

f1f1 f2f2 d o = 15 cm f 1 = 10 cm d i = 30 cm f 2 = 5 cm L = 42 cm d o =12 cm d i = 8.6 cm Net magnification: m net = m 1 m 2

Amazing Eye One of first organs to develop. 100 million Receptors 4 million –200,000 /mm 2 2,500 /mm 2 –Sensitive to single photon! Candle from 12 miles 15 Ciliary Muscles

ACT: Focusing and the Eye Cornea n= 1.38 Lensn = 1.4 Vitreousn = 1.33 Which part of the eye does most of the light bending? 1) Lens2) Cornea3) Retina4) Cones Lens and cornea have similar shape, and index of refraction. Cornea has air/cornea interface 1.38/1, 70% of bending. Lens has Lens/Vitreous interface 1.4/1.33. Lens is important because it can change shape. Laser eye surgery changes Cornea 17 Ciliary Muscles

Eye (Relaxed) 25 mm Determine the focal length of your eye when looking at an object far away. 21 Object is far away: Want image at retina:

Eye (Tensed) 25 mm Determine the focal length of your eye when looking at an object up close (25 cm). 250 mm 25 Object is up close: Want image at retina:

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? 1) 13 cm 2) 26 cm 3) 52 cm 26cm 13cm Preflight % 44% 09% Image from mirror becomes object for eye!

Near Point, Far Point Eye’s lens changes shape (changes f ) –Object at any d o can 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)

If you are nearsighted... Want to have (virtual) image of distant object, d o = , at the far point, d i = -d far. 42 f lens = - d far Too far for near-sighted eye to focus d far Near-sighted eye can focus on this! Contacts form virtual image at far point – becomes object for eye. dodo (far point is too close)

Refractive Power of Lens Diopter = 1/f where f is focal length of lens in meters. Person with far point of 5 meters, would need contacts with focal length –5 meters. Doctor’s prescription reads: 1/(-5m) = –0.20 Diopters 43

If you are farsighted... When object is at d o, lens must create an (virtual) image at -d near. Want the near point to be at d o. 45 Too close for far-sighted eye to focus d near Far-sighted eye can focus on this! dodo Contacts form virtual image at near point – becomes object for eye. (near point is too far)

ACT/Preflight 19.4 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? Does it help if you have a high prescription? 1.nearsighted 2.farsighted Farsighted person’s glasses are converging – like magnifying glass!

Angular Size Preflight 19.6, 19.7 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     46 Both are same size, but nearer one looks bigger.

Unaided Eye Bring object as close as possible (to near point d near ) How big the object looks with unaided eye. ** If  is small and expressed in radians. 47  object d near h0h0

Magnifying glass produces virtual image behind object, allowing you to bring object to a closer d o : and larger  ′ Compare to unaided eye: : Ratio of the two angles is the angular magnification M: Magnifying Glass 48 object virtual image hihi hoho didi dodo magnifying glass

M = d near /d 0 = d near /f +1 For max. magnification, put image at d near : so set d i = -d near : Angular Magnification 50 object virtual image hihi hoho dodo magnifying glass (d near = near point distance from eye.) didi Smaller f means larger magnification See text, Example 24.6 Forthelens: 1 d o  1 d i  1 f  1 d o  1 f  1 d i

See you next Monday