14.1

converging lenses

these lens use refraction to bend light rays -light rays converge after passing a converging lens -rays from a common point on an object converge to a common point on far side of the converging lens

ray tracing for converging lens to find the image created by the lens

(a): ray 1 leaves top point on object going parallel to the axis, then goes through focal point (b) Ray 2 passes through F', therefore it is parallel to the axis beyond the lens (c) ray 3 passes straight through the center of the lens

EX: if you hold a magnifying glass at the proper distance above a sheet of white paper, you will se an image of the overhead room lights on the paper-explain

it is a real image of the room lights, created by the converging magnifying glass. A magnifying glass is a converging lens and can form a real image. It brings light spreading outward from the room lights together onto the sheet of paper as a real image.

lens diameter and focusing

larger lens: converges more light, brighter image, focus becomes more critical, less depth of focus (a) -smaller lens: dimmer image, focus becomes less critical, more depth of focus. (b)

Ex: while taking a photo of your friend, with the diaphragm of your large camera lens wide open, you notice that the background is blurry, explain

light from the more distant background focuses closer to the lens than light from your friend. since the camera is focusing on your friend, the background appears out of focus. When the aperture of your camera is wide open, focusing becomes crucial. Objects in from of or behind your friend are out of four on the image sensor and appear blurry

focusing

light reaching the lens from an object is diverging -the nearer the object, the more its light diverges -converging lens has trouble with diverging light--> real image of nearby object forms farther form lens, real image of distant object forms closer to lens

Ex the eyeglasses of a farsighted person can project a real image of a distant scene on a white wall. However, the eyeglasses of a nearsighted person produce no real image Why not?

nearsighted eyeglasses use diverging lenses, which bend light rays apart and don't focus them together into a real image. To form a real image of distance scene you need to bring light rays together with a converging lens. Diverging lenses spread light rays apart and can't form real images on their own.

focal le

- -lenses are characterized by two quantites: focal length and f number. The focal length of a lens is the distance between the lens and the real image it forms of a very distant onject. For ex: if a real image of the moon forms 100 mm (4 in) behind a particular lens, then that lens ahas a focal length of 100 mm. The focal lengths of camera lenses range from less than 100 mm (.4 in) in many compact cameras to about 2 m (7ft) in cameras used for nature photography. -when light from a scene passes through a short-focal length lens, it comes to a focus near that lens and produces a relatively small image on the image snesor. Because a long focal length lens permits the light passing through it to spread out more before coming to a focus, it produces a larger really image on the sensor. -The "normal" lens for a protocolar camera has a focal length that allows all the objects in your central field of vision to fit onto the image sensor. When you hold the finished put about 30 cm from your eyes, the objects in the picture appear about the same size they did when the photo was taken. The focal length of a camera's normal lens is about 1.5 times that horizontal width of its image sensor --a wide angle lens has a shorter focal length than the normal lens (a). The image it projects on to the image sensor is smaller but brighter, and most of the objects in your entire field of vision appear in the photo. A telephoto lens has a longer focal length than the normal lens (b). The image is projects onto the sensor is larger but dimmer with only objects at the center of the scene appearing in the photo.

lenses and film eyes and retina

-Film records the pattern of light it's exposed to -If you put film in a real image, it will record a pattern of light resembling the object -For a good photograph, the real image should be sharply focused on the film and have the right size -f the sensor is too close to the lens, then the light doesn't have room to come together. If the sensor is too far from the lens, then the light begins to come apart again before reaching the sensor. The candle's real image is only in focus at one distance from the lens

viewfinder and virtual images

-Single lens reflex cameras permit you to change their lenses so that you can choose a lens that's optimized for the task at hand. When you peer through the viewfinder of an SLR camera you're looking at the same real image that will be projected onto the image sensor during the exposure. The light you see travel through the camera's main lens, reflects off a mirror, and projects onto a translucent screen inside the top of the camera. During the exposure, the mirror flips out of the way and the real image projects briefly onto that image sensor. -since the screen and real image are only an inch or two from your eye, you can't focus on them without the help of the eyepiece lens. The eyepiece lens is converging, but in this case it does;t form a real image. Instead it form a virtual image, an image located at a negative image distance—that is on the wrong side of the lens. -The screen displaying the scene that your photographing is so close to the eyepiece lens that the object distance is less than the lens's focal length. According to the lens equation, the image distance should be negative, and it is, the image located on the screen side of the eyepiece lens. You can't put your fingers in the light and project this image on your skin because the image is virtual -you can however see this image through the eyepiece. Its located father away than the screen itself, so your eye can comfortably focus on it. Also, the image is magnified—the eyepiece lens is acting as a magnifying glass. This lens provides magnification because, you you look at the screen through it, the screen image covers a wider portion of your field of vision. This magnification increases as the eyepiece lens's focal length decreases. That's because a shorter-focal length eyepiece lens must be quite close to the screen, where it can bend light rays coming from a smaller region so that they fill your field of vision. The eyepiece lens in a typical camera has been chosen so that the screen fills a comfortable portion of your visual field, allowing you to examine the virtual image in great detail and adjust the lens and camera settings until you have just the right picture in your view. -Cameras with fixed lenses often have two separate viewfinder systmes. A typical digital camera has a small electronic viewfinder, which displays the real imaged being projected onto its image sensor. Although optical viewfinders vary in style and sophisticantion, the best combine real and virtual images. In a real-image optical viewfinder, a system of lenses, mirrors and or presumes produces an erect real image of the scene and you then examine that real image through an eyepiece magnifying glass. The lenses projecting the real image zoom along with the camera' main lens so that what you see through the viewfinder is similar to what the camera's image sensor will record.

near and far site

-a person who is farsighted can't see nearby objects sharp because her lens system has too long a focal length (a) although it can project real images of distant object on her retina, nearby objects focus too far away from the front of her eye and the light strikes her retina before it forms a real image. --to compensate for farsightedess, she wears eyeglass with conversing lenses (b). These lenses begin the task of being light rays together even before they enter her eyes. Her own lens system completes the bending and the real images form closer to the front of her eyes. She is thus able to see nearby object clearly. -a person who is nearsighted is unable to focus on distant because his lens system has too short of a focal length (a). The real images of those distant objects from too close to the from of his eye, and the light has already begun to spread apart by the time it reaches his retina. TO compensate for nearsightedness, he wears eyeglasses with diverging lenses (b). A diverging lens is one that bends light rays apart and therefore has a negative focal length. Typical thinner at its middle than at its edge, a diverging lens beds the nearly parallel rays of light from a distant object so that they diverge more rapidly. Those ray then appear to come from a much nearer object, actually a nearby virtual image, and his eyes are able to focus them properly on his retina.

light from an object

-an illuminated object reflects or scatters light -you see object via this reflected or scattered light -the object's light forms diffuse illumination -you can't tell what object looks like from this diffuse illumination

real image

-an image forms in space on far side of lens -the image is a pattern of light in space that exactly resembles the object except for size and orientation -the image is "real" you can put your hand in it and can capture it on screen

apertature and f number

-aperture characterizes the diameter of the lens -f number is lens focal length (say 35 mm) divided by lens diameter (adjusted by aperture). -larger f number (22 or so on lens) dim image, large depth of filed/focus (focus is forgiving) -small f number (3.5 or so on lens) bright image, small depth of field/focus (focus is critical.

Eyes and Eyeglasses

-each eye consists primarily of a converging lens and an image sensor. In this case, the lens is a combination of the front surface of the eyeball, its cornea, and the internal lens just beneath the cornea. The image sensor is the retina a vast pattern of light sensitive cells and nerves at the back of the eyeball. -when you look at the scene in front of you, the cornea and lens of your eye project a real image of that scene onto your retina and your retina reports the resulting pattern of light to your brain. AS usual, the real image is inverted and reversed left to right, but the brain compensates for that effect -since your eyeball can't alter the distance between the lens and the image sensor, it focuses the real image by adjusting the focal length of the lens. when you look at nearer objects, the lens in your eye becomes more highly curved and its focal length decreases. The light light rays from that nearer object thus converge more sharply and form a real image on your retina. When you view a more distant object, the lens becomes less curved and its focal length increases. -You eye has an iris within its lens system, when you view a bright scene , that iris shrinks to limit the maoist of light striking the retina. As a side effect, your depth of focus increases and everything appears sharper.

focal length

-focal length measures the len's converging ability: long focal length--> weak convergence, long image distance. Short focal length--> strong convergence, short image distance -the larger the object distance, the bigger the image: long focal length--> big images, short focal length: small images. -if the candle moves toward or away from the camera lens, the distance between the lens and the image sensor must also change. When the candle is far away, all its light rays that pass through the lens arrive traveling almost parallel to one another and the inward bend caused by the lens arrive traveling almost parallel to one another and the inward bend caused by the lens make those rays converge together quickly. The rays come into focus relatively near the lens and that where the sensor must be(a). The candle's image on the sensor is much smaller than the candle itself because the light rays have only a short distance over thwack to move up or down after leaving he lens. When the candle is nearby, its light rays that pass through the lens are diverging rapidly and the inward bend caused by the lens is just barely enough to make those rays converge a--> the rays come into focus relatively far from the lens (b). The candle's image on the sensor is quite large because the light rays have considerable distance over which to move up or down after leaving the lens.

parallel rays incident on coverging lens

-light rays get refracted by a lenses, that i: light gets bent by a lens -if the ray come in parallel to the principal axis (object at infinity) they will be focused in the focal point -focal length f -focal length is the same on both sides, even if lens is not symmetric --> first image

lenses

-most important optical device -lenses bend light -lenses can form images of objects -used in glasses, cameras, telescopes, microscopes etc -converging lenses: thicker in the middle than the outside -diverging lenses: thinenr in the middle than the outside

converging lens

-the curved shape of the camera lens allows it to form a real image. Light passing through the upper half of the lens is bent downward, while light passing through the lower half is bent upward. Because the camera lens bends light rays toward one another, its a converging lens. -the upper ray from the candle flame travel horizontally toward the top of the lens. As it enters the lens and slows down, this ray of light bends backward. It bends downward again as it leave the lens and travel downward toward the bottom of the image sensor. -the lower ray from the candle flame travel downward toward the bottom of the lens and bends upward as it enters the lens. It bends upward again as it leave the lens and travels horizontally toward the bottom of the sensor. -these two rays of light each the image sensor at the same point. They are joined there by many other rays from the same part of the candle flam so that a bright spot forms on the image sensor. Overall each part of the candle illuminates a particular spot on the image sensor so the lens creates a couple image of the candle on the sensor

Book: lenses and real iamges

-when you take a picture of the scene in front of you, the lens of your camera bends light from that scene into a real image on a light sensitive surface.

lens

-why a camera needs a lens, a transparent object that uses refraction to form images The light passing through a lens bens twice, once as it enter the glass or plastic and again as it leaves. In a camera lens, the bending process bring such of the light from one point on the candle back together at one point on the sensor.

lens equation and magnification

1. Draw a ray diagram 2. solve for unknowns in the lens equation and magnification. Remember reciprocals 3. the height of the image, hi is positive if the image is upright and negative if the image is inverted relative to the object (h0 is always positive) --in addition to indicating where the image of a distant object forms, the focal length of the camera lens relates the object distance to the image distance. The object distance is the distance between the lens and th object your'e photographing the image distance is the distance between the lens and the real image it forms. —> the lens equation 1/focal length=1/object distance+1/image distance. -according to this equation the image distance for a distance object is equal to the focal length of the lens. When the object is nearby, the image distance becomes larger than the focal length, thats why a era lens moves way from the image sensor as you focus closer. When the object distance becomes less than the focal length, the image distance becomes negative and no real image forms at all--> why you can't focus on an object that's too close to the lens

EX airport screening devices often use X-rays to search for hidden items. These high-energy photons can damage film. How?

X-rays cause radiative transitions in the silver salt crystals. X rays can penetrate through normally opaque objects and reach the film. If a silver salt crystal in the film absorbs an X-ray, it will respond as though it was exposed to visible light. Although most modern screening device use such weak X-ray sources that the effects are minimal, repeated screenings of high-speed film will gradually ruin it.

f number

a lens's f-number characterizes the brightness of the real image that it forms on the image sensor, with smaller f numbers indicating brighter images. The number is calculated by diving the len's focal length by its diameter. = since long focal length lenses naturally produce larger and dimmer images on the imager sensor, the f-number takes into account both the light gathering capacity of the lens and its focal length. Increasing a lens's diameter increases its light gathering capacity and decreases its f number. Increasing a lens's focal length decreases the brightness of its real image and increases the f-number. Doing both at once, leaves the brightness and f-number unchanged. -the diaphragm inside a lens allows you to decrease the len's aperture and thus increase it f number. A factor of 2 increase in f-number corresponds to a factor of 2 decrease in the len's effective diameter and a factor of 4 decreases in the len's light gathering area. When you double the f number of the lens, you must compensate by quadrupling the exposure time.

real image

a pattern of light, projected in space or on a surface, that exactly reproduces that pattern of light in the original scene. Since the real image that's projected looks just like the scene you're photographing, recording the light in that image is equivalent to recording the scene your're photographing. -when the light from a candle falls directly on an image sensor, it produces only diffuse illumination (a). Similarly, you can't tell by looking at a sheet of paper what a chndle looks light because the light that leave the candle travel in all directions and is as likely to hit the top of the paper as it is to hit the bottom. When the lens is inbetween the candle and the sensor, it brings light from each point on the candle back together on the sensor's surface, forming an upside down and board real image of the candle. The distance between the lens and the sensor must be chosen correctly or the image will be blurry.

parallel rays incident on converging and diverging lenses

any lens that is thicker in the center than at the edges will make parallel rays converge to a point and is called a converging lens--> converging first image -any lenses that are thinner in the center are called diverging lenses because they make parallel rays diverge -focal point of diverging lens: point where diverging rays seem to be coming from --> last image

EX: on bright, sunny days your auto camera take photos with large depths of focus, while on dark, overcast days its picture have much smaller depths of focus. What causes this difference?

on a bright day, your camera needs on a small aperture to gather enough light for an exposure, so the depth of focus is large. On a dark day it uses the largest aperture available to gather light and has a small depth of focus. Light gathering and depth of focus go hand in hand. If you must open the aperture of you camera's lens to gather enough light for an exposure, focusing will become critical and you photos will have small depths of focus.

image sensors

on pages

EX: as you move a magnifying glass slowly toward the photo in front of you, you see an inverted image that grows larger and nearer to your eye. This image eventually becomes blurry, and then a new upright and enlarged image appears on the photograph's side of the lens. What's happening?

the lens is initially creating a real image near your eye. This real image moves past you as the lens approaches the photo. Finally the lens is close enough to create an enlarged virtual image of the photo. a magnifying glass forms either a real or virtual image, depending on object distance and the lens's focal length. If the lens and photo are spirited by more than the focal length, the image is real and you see it near your eye. You can touch this inverted image or project it on a piece of paper. If the lens and picture are spirited by less than the focal length, the upright image is virtual and you see it on the far side of the lens.