Physics 102: Lecture 19 Lenses and your EYE Ciliary Muscles 1

3 Cases for Converging Lenses Object Image Inverted Reduced Real Past 2F Image Object Inverted Enlarged Real Between F & 2F Demo 71 Image Object Upright Enlarged Virtual Inside F

Only 1 Case for Diverging Lenses P.A. Image Object F Image is always virtual, upright, and reduced.

Preflight 19.1 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.

Preflight 19.1 Still see entire image (but dimmer)! (35% got correct) “There are still rays from the image bouncing off the lower half of the lens that will project the image. ” 35%, 15%, 55%

Same as mirror equation Lens Equation Same as mirror equation do F P.A. Image Object f F do = distance object is from lens: Positive: object in front of lens Negative: object behind lens di Example di = distance image is from lens: Positive: real image (behind lens) Negative: virtual image (in front of lens) Just like for mirrors If d0 larger, di is smaller, |m| smaller If d0 smaller, di is larger, |m| larger f = focal length lens: Positive: converging lens Negative: diverging lens

Multiple Lenses Example Image from lens 1 becomes object for lens 2 1 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.

Multiple Lenses: Image 1 Example do = 15 cm 1 2 f1 f2 f1 = 10 cm di = 30 cm First find image from lens 1.

Multiple Lenses: Image 2 Example 1 2 do = 15 cm L = 42 cm di = 8.6 cm f1 f2 f1 = 10 cm f2 = 5 cm di = 30 cm do=12 cm Now find image from lens 2. Notice that do could be negative for second lens!

Multiple Lenses: Magnification Example 1 2 do = 15 cm L = 42 cm di = 8.6 cm f1 f2 f1 = 10 cm f2 = 5 cm di = 30 cm do=12 cm Net magnification: mnet = m1 m2

The Eye One of first organs to develop. ~100 million Receptors ~200,000 /mm2 Sensitive to single photon! Candle from 12 miles Ciliary Muscles Numbers in red are for a digital camera Macula/fovea is super sensitive part only sees about 15 degrees http://hyperphysics.phy-astr.gsu.edu/hbase/vision/retina.html#c2

ACT: Focusing and the Eye Ciliary Muscles Cornea n= 1.38 Lens n = 1.4 Vitreous n = 1.33 Which part of the eye does most of the light bending? 1) Lens 2) Cornea 3) Retina 4) 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

Eye (Relaxed) Example 25 mm Determine the focal length of your eye when looking at an object far away. 25 mm ~ 1 inch Object is far away: Want image at retina:

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

Near Point, Far Point Eye’s lens changes shape (changes f ) Object at any do should have image be at retina (di = approx. 25 mm) Can only change shape so much “Near Point” Closest do where image can be at retina Normally, ~25 cm (if far-sighted then further) “Far Point” Furthest do where image can be at retina Normally, infinity (if near-sighted then closer)

Preflight 19.3 Image from mirror becomes object for eye! 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? 26cm 13cm 52% 39% 9% 1) 13 cm 2) 26 cm 3) 52 cm Image from mirror becomes object for eye!

If you are nearsighted... Example (far point is too close) do dfar Too far for near-sighted eye to focus dfar Near-sighted eye can focus on this! Contacts form virtual image at far point – becomes object for eye. do flens = - dfar Want to have (virtual) image of distant object, do = , at the far point, di = -dfar.

Refractive Power of Lens Diopter = 1/f where f is focal length of lens in meters. Example: My prescription reads -6.5 diopters flens = -1/6.5 = -0.154 m = -15.4 cm (a diverging lens) dfar = 15.4 cm (!) My eyes: 6.5 diopters, implies f=-0.15 m (my far point is 0.15 m, or 6”, or 15 cm) Big # means smaller f, more bending (worse eyesight) flens = - dfar

If you are farsighted... Example (near point is too far) do dnear Too close for far-sighted eye to focus Far-sighted eye can focus on this! do Contacts form virtual image at near point – becomes object for eye. dnear Example My near point with far correction: 65 cm Want near point at 25 cm Need 1/f=1/.25-1/.65 1/f=2.5 diopters Want the near point to be at do. When object is at do, lens must create an (virtual) image at -dnear

Farsightedness Example Near point dnear > 25 cm To correct, produce virtual image of object at d0 = 25 cm to the near point (di = dnear) Example: My near prescription reads +2.5 diopters flens = +1/2.5 = 0.4 m = 40 cm therefore dnear = 67 cm (with my far correction)

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? Farsighted person’s glasses are converging – like magnifying glass! nearsighted farsighted 61%, 39% Does it help if you have a high prescription?

Angular Size Preflight 19.6, 19.7 Both are same size, but nearer one looks bigger. q q q q Angular size tells you how large the image is on your retina, and how big it appears to be.

Angular size: Unaided Eye How big the object looks with unaided eye. object h0 q dnear Bring object as close as possible (to near point dnear) **If q is small and expressed in radians.

Magnifying Glass object virtual image hi ho di do magnifying glass Magnifying glass produces virtual image behind object, allowing you to bring object to a closer do: and larger q′ Compare to unaided eye: : Ratio of the two angles is the angular magnification M:

Angular Magnification magnifying glass virtual image object (dnear = near point distance from eye.) hi ho do di For the lens : 1 d o + i = f Þ - For max. magnification, put image at dnear: so set di = -dnear: M = dnear /d0 = dnear/f +1 Smaller f means larger magnification

Summary Lenses The eye Lens equation & magnification Multiple lenses Near & far point Nearsightedness & farsightedness & corrective lenses Angular magnification