Announcements Office hours: My office hours today 2 -3 pm or make an appointment

1. Announcements • Office hours: My office hours today 2 -3 pm • or make an appointment • Final exam Saturday 4/23, 3 – 5 pm, • CUMULATIVE EXAM • Make-up exam, Wednesday 4/20, 5:10 – 7:00 pm, NPB 1220, CUMULATIVE EXAM • Always check out http://www.phys.ufl.edu/courses/phy2054/spring11/ for more announcements • QUESTIONS? PLEASE ASK!

2. Review • Single slit diffraction • In general, destructive interference occurs for a single slit of width for: • m = 1, 2, 3, … • Polarization • Natural light is unpolarized • Polarization occurs through selective absorption, reflection, scattering • Polarization through absorption • Transmission through crossed polarizers: Malus’s Law IT = Io cos2θ • Polarization by reflection • Brewster’s angle n = tan θp

3. Chapter 25 http://static-p4.fotolia.com/ Optical Instruments http://www.misericordia.mb.ca/Programs/ecAnatomy.html

4. Camera • Converging lens • Produces a real image • Image is formed on an electric device • CCD, CMOS • Shutter – exposure time • Aperture – light intensity • Light intensity I ~ D2/f2 • ƒ-number - ratio of lens focal length to diameter • ƒ-number = f/D • ƒ-number  lens “speed” • A lens with a low f-number is a “fast” (and expensive) lens • Camera lenses typcially range from 1.4 -11

5. The Eye • Amazing optical instrument! • The normal eye focuses light and produces a sharp image • Essential parts of the eye • Cornea – light passes through this transparent structure • Aqueous Humor – clear liquid behind the cornea • The pupil • A variable aperture • The crystalline lens • Most of the refraction takes place at the outer surface of the eye • Iris (colored portion of the eye) muscular diaphragm that controls pupil size • The f-number of the eye is from about 2.8 to 16

7. The Eye – Focusing • Accommodation • The eye focuses on an object by varying the shape of the crystalline lens through this process • An important component is the ciliary muscle which is situated in a circle around the rim of the lens • Thin filaments, called zonules, run from this muscle to the edge of the lens • focusing on a distant object • The ciliary muscle is relaxed • The zonules tighten • This causes the lens to flatten, increasing its focal length • For an object at infinity, the focal length of the eye is equal to the fixed distance between lens and retina • This is about 1.7 cm • Focusing on near objects • The ciliary muscles tense • This relaxes the zonules • The lens bulges a bit and the focal length decreases • The image is focused on the retina

8. The Eye – Near and Far Points • near point - closest distance for which the lens can accommodate to focus light on the retina • Typically at age 10, this is about 18 cm • Average is about 25 cm • It increases with age, to 500 cm or more at age 60 • far point - the largest distance for which the lens of the relaxed eye can focus light on the retina • Normal vision has a far point of infinity

9. Farsightedness • Also called hyperopia • The image focuses behind the retina • Can usually see far away objects clearly, but not nearby objects

10. Correcting Farsightedness • A converging lens placed in front of the eye can correct the condition • The lens refracts the incoming rays more toward the principle axis before entering the eye • This allows the rays to converge and focus on the retina

11. Nearsightedness • Also called myopia • In axial myopia the nearsightedness is caused by the lens being too far from the retina • In refractive myopia, the lens-cornea system is too powerful for the normal length of the eye

12. Correcting Nearsightedness • A diverging lens can be used to correct the condition • The lens refracts the rays away from the principle axis before they enter the eye • This allows the rays to focus on the retina

13. Problem 25.11 p 843 The accommodation limits for Nearsighted Nick’s eyes are 18 cm and 80 cm. When he wears his glasses, he can see far away objects clearly. At what minimum distance is he able to see objects clearly?

14. Diopters • Optometrists and ophthalmologists usually prescribe lenses measured in diopters • The power of a lens in diopters equals the inverse of the focal length in meters P = 1/f

15. Simple Magnifier • A simple magnifier consists of a single converging lens • This device is used to increase the apparent size of an object • The size of an image formed on the retina depends on the angle subtended by the eye

16. The Size of a Magnified Image • When an object is placed at the near point, the angle subtended is a maximum • The near point is about 25 cm • When the object is placed near the focal point of a converging lens, the lens forms a virtual, upright, and enlarged image

17. Angular Magnification • Angular magnification is defined as • The angular magnification is at a maximum when the image formed by the lens is at the near point of the eye • q = - 25 cm • Calculated by

18. Problem 25.23 p 844 A leaf of length h is positioned 71 cm in front of a converging lens with a focal length of 39 cm. An observer views the image of the leaf at a position of 1.26 m behind the lens. (a) what is the magnitude of the lateral magnification (the ratio of the image size to the object size) produced by the lens? (b) What angular magnification is achieved by viewing the image of the leaf rather than viewing the leaf directly

19. Answer to 25.11

20. Answer to 25.23