1. Chapter 25 Optical Instruments Conceptual questions: 3,6,7,8,9
Quick quiz: 2
Problem: 10,26,48

2. The Camera
The ƒ-number of a camera is the ratio of the focal length of the lens to its diameter
ƒ = f/D
The ƒ-number is often given as a description of the lens “speed”
The lowest ƒ-number setting on a camera corresponds to the aperture wide open and the maximum possible lens area in use
M=h’/h=-q/p
h’=-hf/p
Camera with small f produces small images

3. The Eye Essential parts of the eye
Cornea – light passes through this transparent structure
Aqueous Humor – clear liquid behind the cornea
The pupil
A variable aperture
An opening in the iris
The crystalline lens
The retina
The retina contains receptors called rods and cones
The Eye

4. Iris The iris is the colored portion of the eye
It is a muscular diaphragm that controls pupil size
The iris regulates the amount of light entering the eye by dilating the pupil in low light conditions and contracting the pupil in high-light conditions
The f-number of the eye is from about 2.8 to 16

5. The Eye – Operation Rods and Cones Accommodation
Chemically adjust their sensitivity according to the prevailing light conditions
The adjustment takes about 15 minutes
This phenomena is “getting used to the dark”
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
1/f = 1/p +1/q for an eye q=1.7 cm

6. The Eye -- Focusing Lens maker’s formulae Lens equation
When the eye focuses on a distant object, the ciliary muscle is relaxed and the zonules tighten, as a result the lens flattens, R1 and R2 increase.
When the eye focuses on near objects, the ciliary muscles tenses, this relaxes the zonules, and the lens bulges a bit and the focal length decreases. The image is focused on the retina.

7. The Eye – Near and Far Points
The near point is the closest distance for which the lens can accommodate to focus light on the retina
Typically at age 10, this is about 18 cm
It increases with age
The far point of the eye represents 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

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

9. 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

10. 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

11. 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

12. Diopters
The power of a lens in diopters equals the inverse of the focal length in meters
P = 1/ƒ

13. Problem 10.
A PERSON HAS THE FAR POINT 84.4 CM FROM THE RIGHT EYE AND 122 CM FROM THE LEFT EYE. FIND THE POWERS FOR THE CORRECTIVE LENSES.

14. The Size of a Magnified Image
Angular magnification
is defined as

15. Magnification by a Lens
With a single lens, it is possible to achieve angular magnification up to about 4 without serious aberrations
With multiple lens, magnifications of up to about 20 can be achieved
The multiple lens can correct for aberrations

16. Compound Microscope
The image formed by the first lens becomes the object for the second lens
The image seen by the eye, I2, is virtual, inverted and very much enlarged

17. Magnifications of the Compound Microscope
The lateral magnification of the objective is
L is the distance between the lenses
The angular magnification of the eyepiece of the microscope is
The overall magnification of the microscope is the product of the individual magnifications

18. Telescopes Two fundamental types of telescopes
Refracting telescope uses a combination of lens to form an image
Reflecting telescope uses a curved mirror and a lens to form an image
Telescopes can be analyzed by considering them to be two optical elements in a row
The image of the first element becomes the object of the second element

19. Refracting Telescope
The two lenses are arranged so that the objective forms a real, inverted image of a distance object
The image is near the focal point of the eyepiece
The two lenses are separated by the distance ƒo + ƒe which corresponds to the length of the tube
The eyepiece forms an enlarged, inverted image of the first image

20. Angular Magnification of a Telescope
The angular magnification depends on the focal lengths of the objective and eyepiece
The limiting angle of resolution depends on the diameter, D, of the aperture

21. Reflecting Telescope, Newtonian Focus
The incoming rays are reflected from the mirror and converge toward point A
At A, a photographic plate or other detector could be placed
A small flat mirror, M, reflects the light toward an opening in the side and passes into an eyepiece

22. Examples of Telescopes
Reflecting Telescopes
Largest in the world are 10 m diameter Keck telescopes on Mauna Kea in Hawaii
Largest single mirror in US is 5 m diameter on Mount Palomar in California
Refracting Telescopes
Largest in the world is Yerkes Observatory in Wisconsin
Has a 1 m diameter

23. Resolution with Circular Apertures
The diffraction pattern of a circular aperture consists of a central, circular bright region surrounded by progressively fainter rings
The limiting angle of resolution depends on the diameter, D, of the aperture

24. Resolution
For the images to be resolved, the angle subtended by the two sources at the slit must greater than θmin

25. QUICK QUIZ 25.2
Suppose you are observing a binary star with a telescope and are having difficulty resolving the two stars. You decide to use a colored filter to help you. Should you choose a blue filter or a red filter?

26. Michelson Interferometer
One ray is reflected to M1 and the other transmitted to M2
After reflecting, the rays combine to form an interference pattern
The glass plate ensures both rays travel the same distance through glass

27. Measurements with a Michelson Interferometer
The interference pattern for the two rays is determined by the difference in their path lengths
When M1 is moved a distance of λ/4, successive light and dark fringes are formed
This change in a fringe from light to dark is called fringe shift
The wavelength can be measured by counting the number of fringe shifts for a measured displacement of M
If the wavelength is accurately known, the mirror displacement can be determined to within a fraction of the wavelength

28. Conceptual questions
6. Compare and contrast the eye and a camera. What parts of the camera correspond to the iris, the retina, and the cornea of the eye?
3. The optic nerve and the brain invert the image formed on the retina. Why do we not see everything upside down?
8. If you want to use a converging lens to set fire to a piece of paper, why should the light source be farther from the lens than its focal point?
7. Large telescopes are usually reflecting rather than refracting. List some reasons for this choice.
9. Explain why it is theoretically impossible to see an object as small as an atom regardless of the quality of the light microscope being used.

29. Problem 25.26
A certain telescope has an objective of focal length cm. If the Moon is used as an object, a 1.0 cm long image formed by the objective corresponds to what distance, in miles, on the Moon? Assume 3.8 × 108 m for the Earth–Moon distance.

30. Problem 25-48
A person with a nearsighted eye has near and far points of 16 cm and 25 cm, respectively. (a) Assuming a lens is placed 2.0 cm from the eye, what power must the lens have to correct this condition? (b) Suppose that contact lenses placed directly on the cornea are used to correct the person’s eye. What is the power of the lens required in this case, and what is the new near point? [Hint: The contact lens and the eyeglass lens require slightly different powers because they are at different distances from the eye.]