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

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

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

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

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

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.

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

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

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

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

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

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

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.

The Size of a Magnified Image Angular magnification is defined as

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

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

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

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

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

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

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

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

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

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

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?

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

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

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.

Problem 25.26 A certain telescope has an objective of focal length 1 500 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.

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.]