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Physics: Chapter 12 Notes

Chapter 12.1—CHARACTERISTICS OF LENSES

• a lens is a transparent object with at least one curved side that causes light to refract
• like mirrors, lenses have surfaces defined as concave and convex

DESCRIBING LENSES

• reading stones were the first known lenses, and they were used to magnify print on a page
• plane, concave, and convex are used to describe lenses as well as mirrors; however, lenses have two sides, and either side can be plane, concave, or convex
• there are two classes of lenses:
• diverging lenses cause parallel light rays to spread away from a common point
• they have one to two concave surfaces and are thinner in the centre than on the edges
• converging lenses cause parallel light rays to come together toward a common point
• they have one or two convex surfaces and are thicker in the centre than on the edges
• a piece of glass that has two plane sides causes light rays to neither diverge nor converge
• ex: piece of glass with no curves (window pane)
• when light enters a piece of glass with a plane surface, the rays will bend toward the normal; when the light leaves the glass, it will bend away from the normal by the same amount that they bent toward the normal
• all rays shift to the side, but when they leave the glass, they are travelling in the same direction as when they entered
• since there is no change in the direction of the rays relative to each other, this piece of glass is not considered a lens

CONVERGING LENS

• a lens that brings parallel light rays toward a common point
• example: biconvex lens (is convex on both sides of lens)
• when the rays are incident on the surface on the left side of the lens, they move from a fast medium to a slow medium
• this causes the refracted rays to move toward the normal, causing the rays to converge slightly
• when the light rays leave the second surface of the lens, they move from a slow medium to a fast medium (refracting away from normal)
• because of the direction of the normals at this surface, the rays continue to converge
• when parallel light rays exit a converging lens, they are travelling toward each other

DIVERGING LENS

• a lens that spreads parallel light rays away from a common point
• example: biconcave lens (is concave on both sides)
• parallel light rays refract at each surface of the biconcave lens
• when parallel light rays exit a diverging lens, they are travelling away from each other

FOCALPOINT AND FOCAL LENGTH OF LENSES

• the principal axis of a lens is a straight line that passes through the centre of the lens, normal to both surfaces of the lens
• when rays that are parallel to the principal axis pass through a converging lens, the rays intersect at a point
• this point is called the focal point
• when parallel rays pass through a diverging lens, the rays diverge—only by tracing the rays backward do we see that they converge to a point
• this point is called the virtual focus
• because light can pass through a lens from either side, there are actually two focal points for a lens (they are the same distance from the centre of the lens)
• the position for the focal point for a lens depends on both the index of refraction of the lens material and curvature
• lenses with the same shape but with higher indices of refraction bend rays more (making the focal point closer to the lens)
• lenses with larger curvature but with the same index of refraction have the same effect (focal point is close to lens, as curvature increases causing light to bend more)

THICK AND THIN LENSES

• lenses produce spherical aberration just like curved mirrors
• if the light rays from an object strike a curved mirror very far from the principal axis
• if the lenses are very thin, the effect is not noticeable
• for thick lenses, light rays that pass through the lens near the principal axis will meet at the focal point to form a sharp image
• chromatic aberration is the dispersion of light through a lens
• the rays farther that are farther from the principal axis of a lens don’t pass through the focal point
• the edges of lenses are similar in shape to prisms, so the edges disperse the light into colours
• spherical and chromatic aberration is thick lenses reduces the quality of images (ex: in cameras)
• spherical and chromatic aberration can be partially corrected by combining one or more lenses, especially if the lenses are made of materials with different indices of refraction
• high quality lenses for expensive cameras usually use a combination of many lenses to reduce aberration as much as possible
• aberrations are not significant if lenses are very thin

Chapter 12.2—Images Formed by Lenses

• using ray diagrams, you can predict the location, orientation, size and type of image as it appears through a lens
• similar to mirrors, once the focal point has been identified, three key rays (chosen close to the principal axis) can locate the image of an object

RAY DIAGRAMS FOR CONVERGING LENSES

• the ray diagrams are simplified, because:
• partial reflection and refraction is ignored
• the refraction that should occur at each surface of the lens is replaced with only one bend at the axis of symmetry of the lens
• diagrams on page 495
• optical centre acts like flat glasslateral displacement

IMAGE CHARACTERISTICS IN CONVERGING LENSES

• if object is between F and lens (example: magnifying glass)
• Size: bigger than object
• Altitude: upright
• Location: beyond F on sae side of lens as object
• Type: virtual (light rays needed to be extended)
• if object is between 2F and F
• Size: bigger than object
• Altitude: inverted
• Location: beyond 2F on opposite side of lens as object
• Type: real
• if object is beyond 2F
• Size: smaller than object
• Altitude: inverted
• Location: between F and 2F on opposite side of object
• Type: real

DRAWING RAY DIAGRAMS FOR DIVERGIN LOENSES

• refer to textbook page 497 for diagrams

IMAGE CHARCTERISTICS IN DIVERGING LENSES

• the image for a diverging lens will always be the same, no matter where the object is place:
• Size: smaller than object
• however, the farther the object is from the lens, the smaller the image
• Altitude: upright
• Location: closer to the lens than the object; on the same side of the lens; in front of object
• Type: virtual

THIN LENS AND MAGNIFICATION EQUATION

• as with mirrors, you can use algebraic equations to predict the position and size of the images formed by lenses
• the symbols used in the equations represent:
• f = focal length
• do = distance of object from the lens
• di = distance of image from the lens
• ho = height of object
• hi = height of image
• the thin lens equation is the same equation as the mirrors equation
• the magnification equation is the same as the magnification equation for mirrors
• the negative sign means that real images are inverted
• for virtual images, the image distance is negative; the negative sign in the equation ensures the height of the image to be positive (ALL VIRTUAL IMAGES ARE UPRIGHT)

GRAVITATIONAL LENSES

• Albert Einstein proposed that gravity can bend light
• you need a huge galaxy or collection of galaxies to witness this effect
• if there was an extremely bright galaxy directly behind a huge galaxy (relative to earth), the light from the extremely bright galaxy would be bent around the huge galaxy
• an observer would see the light as a ring around the huge galaxy

Chapter 12.3—Lens Technologies and the Human Eye

TELESCOPE MODIFICATIONS

• Johannes Kepler modified the design of Galileo’s telescope to get greater magnification, but his changes also inverted the image
• Galileo’s telescope used two lenses—a converging and a diverging lens
• converging lens was the objective lens (the lens through which light enters a telescope)
• the diverging lens was the eyepiece—the lens in a telescope through which the observer views the object and through which light leaves the telescope

RAY DIAGRAMS FOR TELESCOPES

• the two lenses are positioned so that the focal points to the right of both lenses are in the same place
• the focal points of the lenses are at the same point: past the eye piece
• if there was only an objective lens, the object would be inverted; the eyepiece makes the image upright
• steps:
• light enters the telescope via the objective lens and forms an image between the two lenses
• the image formed by the objective lens becomes the object for the eyepiece lens—light rays from the first image then passes through the eyepiece lens and forms a virtual image that appears to come from just beyond the objective lens
• light from the first image then passes through the eyepiece lens and forms a virtual image that appears to come from just beyond the objective
• the final image is inverted, and is larger than the image formed by the objective lens
• for ray diagrams, refer to textbook page 503

Newton’s Innovation

• his telescope significantly reduced the chromatic aberration by using a concave mirror as the objective lens
• light enters the telescope and travels to the concave mirror objective
• the mirror reflects the light toward focal point (behind the plane mirror)
• before the rays reach focal point (behind the mirror),l the light is reflected off of the plane mirror
• where the reflected rays (from plane mirror) meet is the focal point for the eye piece lens (rays from this focal point pass through the eyepiece, and magnifies the image)
• for diagram, refer to textbook page 504

Modern Telescopes

• although there have been many advances in the telescope, all modern telescopes are based on the designs of Galileo, Kepler, and Newton
• the ones based on Galileo and Kepler are called refracting telescopes (because they use only lenses)
• the ones based on Newton are called reflecting telescopes (because a mirror is included)
• an important feature of all optical telescopes is the amount of light that they are able to collect
• if too little light is collected, a star might be in the field of view but still not able to be seen
• the only way to allow in more light is to make the objective lens or mirror as large as possible but still maintain a precise shape
• a large objective lens is more difficult to make than a larger mirror, so most large, modern telescopes are reflecting telescopes

BINOCULARS

• binoculars are 2 refracting telescopes based on Kepler’s design
• both eyes see the same image
• binoculars have two prisms on each side that use total internal reflection
• reflecting through the prisms makes the light path longer—the longer light path provides better magnification
• the prisms are oriented such that the image is upright when it reaches the observer’s eye

MICROSCOPES

• purpose of a microscope is to make a tiny specimen, larger
• steps:
• rays from the specimen pass through the objective lens, and the refracted rays form an inverted, real image between the lenses
• rays from the image pass through the eyepiece, which again refracts the rays, this forming the final inverted virtual image
• ray diagram on textbook page 505

SIGHT AND THE HUMAN EYE

• the larger the eye, the more light it can collect
• the human eye can focus on objects at different distances, record images, and detect subtle changes in colours and brightness
• the focussing happens at the front of the eye, while everything else happens at the back of the eye and in the brain
• the 2 important parts of the eye:
• cornea—tissue that forms a transparent, curved structure in the front of the eye; refracts light before it enters the eye
• retina—a layer of rod and cone cells that respond to light and initiate nerve impulses; rod cells are very sensitive to light but can’t distinguish between colours; cone cells detect colour
• in a lens, when an object is moved, the image also moves—in the eye, the distance between the retina and the lens are always the same
• the cornea reflects light in the same way regardless of the location of the object
• the lens in your eye can change shape and thus refract light to different extents, allowing it to focus light from both nearby and faraway objects at the retina
• the ciliary muscles make the lens shorter and thicker
• the relaxed normal eye lens focuses a distant object correctly on the retina; a shorter and thicker lens is used to focus on nearby objects

COMPARING THE EYE AND THE CAMERA

• camera is designed very much like an eye
• both have lenses that focus light on a light-sensitive material
• the lens of the eye changes shape in order to focus on objects at different distances
• the lens of the camera must be moved in and out to focus on objects at different distances
• in the camera, the light-sensitive material is either film or CCDs; in the eye, the retina is the light-sensitive tissue
• the camera has an aperture that controls the amount of light that enters the camera; the pupil controls the amount of light that enters the eye

CORRECTING VISION USING LENSES

• common causes of poor vision are an incorrect shape of the eyeball, and incorrect shape of the cornea, and hardening of the lens
• each condition can be corrected by eyeglasses/contact lenses
• most can be corrected by laser surgery
• myopia (near-sightedness) is the condition in which the eye can’t focus on distant objects
• the cornea and eye lens refract the light and brings the rays together; however the eyeball is too long, and the image forms in front of the retina
• by the time they reach the retina, they have begun to spread out again, and the image is blurry
• a diverging lens spreads out the parallel rays before reaching the eye; the rays that are separating from each other appear to be coming from an object that is closer to the eye
• when the eye refracts the light, it is focussed on the retina
• hyperopia (far-sightedness) is the condition in which the eye cannot focus on nearby objects
• people who are far sighted can’t read the print on the page
• the eye can’t focus on nearby objects—the light coming from nearby objects is refracted by the cornea and eye lens
• this means the eyeball is too short—as a result, the rays reach the retina BEFORE they meet, causing the image to be blurry
• far-sightedness can be corrected with a converging lens—the corrective lens bends the rays a little, bringing them closer together before they reach the cornea
• the lens of the eye then refracts the rays a little more, and the rays are focuses in the retina
• presbyopia is the condition in which the lenses of the eye become stiff and the cilliary muscles can no longer make the lenses change shape
• usually happens as a person ages
• those who have it can’t focus on nearby objects
• when people are near-sighted and have presbyopia, they can’t focus on either distant or nearby objects
• to correct this condition, people wear bifocal glasses/contact lenses—lenses with two parts (top part is a lens that corrects near-sightedness, and a small section of the lower part helps the eyes focus on nearby objects
• astigmatism is the blurred or distorted vision usually caused by an incorrectly shaped cornea
• instead of being rounded, the cornea is oval
• part of an image might be in focus while the rest is blurry

Handouts

LENS TERMINOLOGY

• the line in the middle of the lens is called the axis of symmetry
• optical centre—where the axis of symmetry and principal axis meet
• emergent ray
• ignore refraction when doing lens diagrams, as the lenses are thin (which means very very little refraction)

S.A.L.T. FOR CONVERGING LENSES

 Object Location Size of Image Attitude of Image Location of Image Type of Image Beyond 2F smaller than object inverted opposite side of object (between F and 2F) real At 2F smaller than object inverted opposite side of object (between F and 2F) real Between 2F and F bigger than object inverted opposite side of object (beyond F) real At F NO IMAGE NO IMAGE NO IMAGE NO IMAGE Between F and Lens bigger than object upright same side as object; behind the object virtual

S.A.L.T. FOR CONVERGING LENSES

• Size: smaller than object
• however, the farther the object is from the lens, the smaller the image
• Altitude: upright
• Location: closer to the lens than the object; on the opposite side of the lens
• Type: virtual

THE EYE

• the human eye normally focuses the image of an object on the retina
• structures to know: cornea, iris (coloured tissue that controls the amount of light entering), pupil, lens, retina (real image formed here)
• lenses with a larger curvature bends light rays more than those with smaller curvatures
• therefore, thicker lenses have smaller focal lengths
• as you get older, the eye lens loses the ability to change shape
• the lens in our eyes also changes shape
• when we look at far objects, the ciliary muscle is stretched, causing lens to be thin (far focal point)
• when we look at objects nearby, the muscles relax, causing the lens to be round and thicken (focal point is near the lens)

• corrective diverging lens—light diverges slightly so lens can focus light further (at retina)
• corrective diverging lens—lens helps light focus earlier (at retina0