An Application of Lenses: The Human Eye. Prof. Jodi Cooley Supplementary Material for PHY1308 (General Physics Electricity and Magnetism)

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1 An Application of Lenses: The Human Eye Prof. Jodi Cooley Supplementary Material for PHY1308 (General Physics Electricity and Magnetism)

2 Announcements Homework 13 Assigned - Due before 3 pm on Friday November 30th ONLINE ONLY. Final Cumulative Exam Date: Friday, December 7th at 8 am - 11 am Location: FOSC 158 (our regular classroom) Cumulative 3 hour exam covers material from entire semester. The exam will have 4 sections corresponding to each part of the course. There is an opportunity to replace your lowest midterm exam score with the score of the corresponding section on the final exam if the final exam score on that corresponding section is higher than your midterm exam score. Keep going! You can do it!

3 THE HUMAN EYE

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5 Sign conventions of the radii of curvature of the sides of a thick lens. R1 is the radius of curvature of the side closest to the object. R2 is the radius of curvature of the side farther from the object.

6 The Lens-Maker's Equation (Thin Lens) 1 R2 )

7 The Lens-Maker's Equation (Thick Lens) Consider a lens surrounded by air, so n0 = Assume material thickness (widest part, on the optical axis of the lens) is d : ( 1 1 (n 1)d =(nlens 1) + f lens R1 R 2 nr 1 R2 1 )

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9 Vitreous humor Aqueous humor Cornea: provides about 2/3 of the eye's Optical Power (more about that later), and is a fixed-lens system. Lens: provides the remaining power and is adjustable by musculature.

10 Cornea: mostly albumin Aqueous Humor: 98% water Lens: transparent cells, with no nuclei or organelles, arranged in long fibers.

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12 Near-sighted: cannot see distant objects Near-sighted: corrective optics corrective optics that make objects look closer than they actually are so that the eye can focus on them. MYOPIA

13 Far-sighted: cannot see close objects Far-sighted: corrective optics Location of virtual image from corrective converging lens (i<0), which the eye can then see. Virtual image is further away than object. HYPEROPIA Far-sighted individuals need corrective optics that make objects look further away than they actually are so that the eye can focus on them.

14 LASIK (laser-assisted in situ keratomileusis)

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17 The Blind Spot Left Eye A O X

18 The Blind Spot Right Eye X O A

19 Eye vs. Eye Vertebrate vs. Octopus

20 Light Detection The Fovea is a central pit in the eye containing most of your Cone Cells, the ones sensitive to bright-light conditions that give you most of your vision. The Rod Cells give you lowlight vision (note that they are spread out over far more of the back of the eye than the cones). Number of receptors per mm² Angle from fovea Genetic mutations alter the specific properties of the three 80 color-sensitive pigments in cones...

21 What Color is the Dress? Color #1 Red: 125 Green: 145 Blue: 175 Color #2 Red: 87 Green: 70 Blue: 55

22 The Near Point Definition: the closest distance that an object can be brought toward the eye and still have the eye focus the image. Near Point For corrective lenses, the near point is usually assumed to be 25cm standard for a normal person with healthy eyesight. Normal age-related changes to the lens between ages lead to the first signs of Presbyopia, making it hard to read small print in dim light (for instance). This may require additional corrections.

23 Reading Glasses and Power Reading glasses are sold in different powers, measured in Diopters, D. Diopters are just m-1 inverse distance units. The power of reading glasses is determined by the inverse of the lenses' focal length. Normal human eye optical power: 60 D (1/60D = 0.017m) Up to about age 25, you can adjust your focal length by up to 20 additional diopters; by age 25, this reduces to 10 D. By age 50, you can adjust by only 1 D as the lens continues to age. Over-the-counter reading glasses are sold in 0.25D increments simple trial-and-error allows you to pick out your own reading glasses. Diopters are convenient because of the lens equation, and stacking lenses of various powers means just summing to get the result.

24 How to Calculate Your Corrective Power You are farsighted (hyperopic), and can only read clearly objects that are a MINIMUM distance of 70cm from your eyes. How do you figure out what reading glasses you need? Easy! You WANT lenses that will make an object placed at 25cm (the near point) APPEAR to be at 70cm, so your eyes can form a clear image. Thus: KNOW IT! 1/i = 1/(-70cm) = -1.43D = i p f KNOW IT! 1/p = 1/(25cm)=4D WANT IT! 1/f = -1.43D + 4D = 2.57D

25 And Shop!

26 Glasses and Contact Prescription EYE SPHERICAL CYLINDRICAL AXIS OD x15 OS PL x85 OD: Oculus Dexter, Latin for Right Eye OS: Oculus Sinister, Latin for Left Eye PL: Plano, meaning no refractive error. Spherical: the main correction, assuming a spherical lens (diopters) Cylindrical: the fine tuning, needed for things like astigmatism (diopters) Axis: the axis of the astigmatism the directional blur in vision. This is in degrees.

27 What about me? With my glasses or contacts OFF, I have to hold text at a distance of 40cm or less to focus it, and my near point is 12cm. With my glasses ON, my near point is 16.5cm. I want my corrective optics to make an image of something held at arm's length (about 70cm) that appears at 40cm, so I can focus on that image. Thus: 1/(70cm) + 1/(-40cm) = 1/f = -1.34D My actual contact prescription has a spherical power of -1.5D. Not bad!

28 Conclusions The eye is a complex lens system It has inherent flaws, and flaws that appear with age Physics lets us correct the flaws of the eye corrective lenses glasses and contacts laser-based corneal sculpting surgical procedures The complex biochemistry and biophysics of the eye also arises from genetic variation e.g. color perception due to variations in the pigments that give cone cells color distinction.

29 The End! xkcd: 1308: Christmas Lights