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Final exam Saturday 4/23, 3 – 5 pm,
CUMULATIVE EXAM
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2. Review Single slit diffraction m = 1, 2, 3, … Polarization
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 cos2 θ
Polarization by reflection
Brewster’s angle
n = tan θp

3. Chapter 25 Optical Instruments http://static-p4.fotolia.com/

4. Camera Converging lens Image is formed on an electric device
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

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 focusing on a distant object
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 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 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