The eye & corrective lenses
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1 Phys 102 Lecture 20 The eye & corrective lenses 1
2 Today we will... Apply concepts from ray optics & lenses Simple optical instruments the camera & the eye Learn about the human eye Accommodation Myopia, hyperopia, and corrective lenses Learn about perception of size Angular size Magnifying glass & angular magnification Phys. 102, Lecture 19, Slide 2
3 The Camera Cameras are one of simplest optical instruments, produce real image onto sensor Pinhole camera ( camera obscura ) Modern camera Pinhole DEMO Imaging lens = do di flens Not a true imaging system. Each point from object creates a circle of light on screen. True imaging system. Each point from object has a corresponding point on screen. Phys. 102, Lecture 20, Slide 3
4 Evolution of the eye The eye is like a camera Pinhole eye Complex eye Nautilus Octopus Phys. 102, Lecture 20, Slide 4
5 Anatomy of the human eye As in a camera, eye lens creates image of object onto retina Ciliary muscles Cornea Pupil Iris Vitreous fluid Retina Lens Optic nerve Part of eye n Cornea Lens Vitreous fluid Pupil controls amount of light diameter typically 2 8 mm Retina has ~125 million photoreceptor cells (rods & cones) DEMO Phys. 102, Lecture 20, Slide 5
6 ACT: Anatomy of the Eye Which part of the eye is responsible for most of the bending of light? Cornea Vitreous fluid Lens Retina Part of eye n Cornea Lens Vitreous fluid A. Lens B. Cornea C. Retina D. Vitreous fluid Phys. 102, Lecture 20, Slide 6
7 Accommodation Ciliary muscles around lens change its shape and focal length The eye can focus on objects both close and far Ciliary muscles Distant object Close object Relaxed lens Image The far point and near point are the maximum and minimum object distances where the image remains in focus Far point: d o,far = Near point: d o,near = 25 cm Normal adult DEMO Phys. 102, Lecture 20, Slide 7
8 Calculation: focal length of the eye An adult with normal eyesight will see a focused image over a wide range of object distances: Far point: d o,far = Near point: d o,near = 25 cm Object d o d i Image Typical lens retina distance = 2.0 cm What are the focal lengths of the relaxed and tensed eye? Phys. 102, Lecture 20, Slide 8
9 ACT: CheckPoint 1 A person with almost 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? A. 13 cm B. 26 cm C. 52 cm Phys. 102, Lecture 20, Slide 9
10 Near Point, Far Point Eye s lens changes shape (changes f ) Object at any d o should produce image at retina (d i 2.0 cm) Lens can only change shape so much Far Point Furthest d o where image can be at retina Normally, d far = (if nearsighted then closer) Near Point Closest d o where image can be at retina Normally, d near 25 cm (if farsighted then further) Phys. 102, Lecture 20, Slide 10
11 Myopia (nearsightedness) If nearsighted, far point d far < Image Distant object Far point Object at d o > d far creates image in front of retina Corrective lens creates image of distant object at the far point of the nearsighted eye = d d f o far lens f lens = d far f lens such that distant object at ( normal far point) is in focus lens DEMO Phys. 102, Lecture 20, Slide 11
12 Hyperopia (farsightedness) If farsighted, near point d near > 25 cm Near point Close object Image Object at d o < d near creates image behind retina Corrective lens creates image of close object at the near point of the farsighted eye = d d f o near lens d > 25cm so near f lens > 0 f lens such that object at 25 cm ( normal near point) is in focus lens DEMO Phys. 102, Lecture 20, Slide 12
13 ACT: Corrective lenses For which type of eye correction is the image always virtual? Nearsighted eye Farsighted eye A. Nearsighted B. Farsighted C. Both D. Neither Phys. 102, Lecture 20, Slide 13
14 Calculation: Refractive Power Optometrists use refractive power P instead of focal length f P 1 f Units: Diopters (D) 1/meters Your friend s contact lens prescription is 3.3 diopters. What is the focal length? Is your friend near or farsighted? f lens = 1 P Phys. 102, Lecture 20, Slide 14
15 ACT: Refractive power A relaxed, normal eye has a refractive power P norm : P norm = D f = 0.02 m =+ norm How does the refractive power P myopic of a relaxed, nearsighted eye compare? A. P myopic > +50 D B. P myopic = +50 D C. P myopic < +50 D Phys. 102, Lecture 20, Slide 15
16 ACT: CheckPoint 2 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? A. Nearsighted B. Farsighted Phys. 102, Lecture 20, Slide 16
17 Astigmatism A normal eye is spherical, curved the same in every direction An astigmatic eye is distorted (oval) along one direction g y ( ) g Rays from vertical object Vertical Image Rays from horizontal object Horizontal Image So, an astigmatic eye has a different f along different directions Images are blurry in one direction Corrected with toric lens Phys. 102, Lecture 20, Slide 17
18 Angular Size: CheckPoint Angular size refers to how large the image is on your retina, and how big it appears to be. h o θ θ θ' θ' d o Both objects are same size, but nearer one looks bigger. θ h d o o (in radians) if angle is small What is the maximum possible angular size? Phys. 102, Lecture 20, Slide 18
19 Calculation: Angular size A cameraman takes a trick shot of the Eiffel tower, which is 300 m tall. How far is the cameraman from the Eiffel tower? (Assume the camera is 30 cm from his hand.) h = 10 cm 300m θ h = 0.1m 0.3m Phys. 102, Lecture 20, Slide 19
20 Magnifying glass A magnifying glass produces a virtual image behind object, allowing a closer object d o < d near and a larger θ h i Virtual image h o θ' h i θ θ d i = h o d o Near point d o d i Angular magnification gives how much angular size increases: θ h d o o M = θ max h o d near = d d near o = d near f Typically set image at d i =, for a relaxed eye (so d o = f) Phys. 102, Lecture 20, Slide 20
21 ACT: Magnifying glass A person with normal vision (d near = 25 cm, d far = ) has a set of lenses with different focal lengths. She wants to use one as a magnifying glass. Which of the following focal lengths will work? A. f = 50 cm B. f = 2.5 cm C. f = 6 cm D. f = 40 cm DEMO Phys. 102, Lecture 20, Slide 21
22 Summary of today s lecture Accommodation eye lens changes shape Near point closest object (~25 cm, further if farsighted) Far point furthest object (, closer if nearsighted) Corrective lenses Nearsighted diverging lens creates virtual image at far point Farsighted converging lens creates virtual image at near point Angular size & angular magnification Magnifying glass creates virtual image of object placed closer than near point Phys. 102, Lecture 20, Slide 22
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