Chapter 23 the Refraction of Light: Lenses and Optical Instruments
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Object-Image Real Image Virtual Image
Object-Image • A physical object is usually observed by reflected light that diverges from the object. • An optical system (mirrors or lenses) can 3.1 Images formed by Mirrors and Lenses produce an image of the object by redirecting the light. • Images – Real Image • Image formation by mirrors – Virtual Image • Images formed by lenses Real Image Virtual Image Optical System ing diverging erg converging diverging diverging div Object Object real Image Optical System virtual Image Light appears to come from the virtual image but does not Light passes through the real image pass through the virtual image Film at the position of the real image is exposed. Film at the position of the virtual image is not exposed. Each point on the image can be determined Image formed by a plane mirror. by tracing 2 rays from the object. B p q B’ Object Image The virtual image is formed directly behind the object image mirror. Light does not A pass through A’ the image mirror A virtual image is formed by a plane mirror at a distance q behind the mirror. q = -p 1 Parabolic Mirrors Parabolic Reflector Optic Axis Parallel rays reflected by a parabolic mirror are focused at a point, called the Parabolic mirrors can be used to focus incoming parallel rays to a small area Focal Point located on the optic axis. or to direct rays diverging from a small area into parallel rays. Spherical mirrors Parallel beams focus at the focal point of a Concave Mirror. •Spherical mirrors are much easier to fabricate than parabolic mirrors • A spherical mirror is an approximation of a parabolic Focal point mirror for small curvatures. -
Lab 11: the Compound Microscope
OPTI 202L - Geometrical and Instrumental Optics Lab 9-1 LAB 9: THE COMPOUND MICROSCOPE The microscope is a widely used optical instrument. In its simplest form, it consists of two lenses Fig. 9.1. An objective forms a real inverted image of an object, which is a finite distance in front of the lens. This image in turn becomes the object for the ocular, or eyepiece. The eyepiece forms the final image which is virtual, and magnified. The overall magnification is the product of the individual magnifications of the objective and the eyepiece. Figure 9.1. Images in a compound microscope. To illustrate the concept, use a 38 mm focal length lens (KPX079) as the objective, and a 50 mm focal length lens (KBX052) as the eyepiece. Set them up on the optical rail and adjust them until you see an inverted and magnified image of an illuminated object. Note the intermediate real image by inserting a piece of paper between the lenses. Q1 ● Can you demonstrate the final image by holding a piece of paper behind the eyepiece? Why or why not? The eyepiece functions as a magnifying glass, or simple magnifier. In effect, your eye looks into the eyepiece, and in turn the eyepiece looks into the optical system--be it a compound microscope, a spotting scope, telescope, or binocular. In all cases, the eyepiece doesn't view an actual object, but rather some intermediate image formed by the "front" part of the optical system. With telescopes, this intermediate image may be real or virtual. With the compound microscope, this intermediate image is real, formed by the objective lens. -
Lens Equation – Thin Lens
h s’ s f h’ Refraction on Spherical Surface θa=α +φ ; φ = β +θb ⎫ an sinθ a= n bsinθ b n⎬aα + n bβ = ( n b− )φ n a anθ a≅ n b θ b ⎭ h h h tanα = ; tanβ = ; tanφ = s + δ s'−δ R − δ h h h n n n− n ≅α ; β ≅; φ ≅ ⇒a+ b = b a s s' R s s' R Refraction on Spherical Surface n n n− n a+ b = b a Magnification s s' R R positive if C on transmission side; negative otherwise y − y′ tanθ = tanθ = na y nb y′ a b = − s s′ s s′ nasinθ a= n bsin θ b y′ na ′ s esl angallFor sm m = = − y n s tanθ≅ sin θ b Refraction on Spherical Surface n n n− n a+ b = b a . A fish is 7.5Example: Fish bowl s s' R cm from the front of the bowl. y′ n′ s Find the location and magnification of the m = = − a fish as seen by the cat.bowl. Ignore effect of y nb s Radius of bowl = 15 cm. na = 1.33 R negative b O n n n− n n n− n n I s’ a+ b =b a b = b a− a s s' R s' R s s n 1 s′ = b = =6 .− 44cm n− n n 0− . 331 . 33 a b a− a − R s −cm15 7 . 5 cm n′ s 1 .( 33 6− . 44cm ) The fish appears closer and larger. m= − a= − ∗ 1= . 14 nb s 1 7 .cm 5 Lenses • A lens is a piece of transparent material shaped such that parallel light rays are refracted towards a point, a focus: – Convergent Lens Positive f » light moving from air into glass will move toward the normal » light moving from glass back into air will move away from the normal » real focus Negative f – Divergent Lens » light moving from air into glass will move toward the normal » light moving from glass back into air will move away from the normal » virtual focus Lens Equation – thin lens n n n− n n n n− n a b+ b = a b+ a = a b 1s s 1' R 1 2s s 2' R2 For air, na=1 and glass, nb=n, and s2=-s1’. -
Location of Cardinal Points from the ABCD Matrix for the General Optical System
EE482 Fall 2000 Handout #2 Page 1 Location of Cardinal Points from the ABCD Matrix for the General Optical System I II n1 n2 F1 P1 N1 P2 N2 F2 f1 f2 Figure 1 Cardinal points of a system which is characterized by an ABCD matrix between an input plane I and an output plane II. Cardinal Point Measured Function Special Case From To (n1=n2) First Focal Point P1 F1 -n1/(n2C)-1/C First Principle Point I P1 (n1-n2D)/(n2C)(1-D)/C First Nodal Point I N1 (1-D)/C (1-D)/C Second Focal Point P2 F2 -1/C -1/C Second Principle Point II P2 (1-A)/C (1-A)/C Second Nodal Point II N2 (n1-n2A)/(n2C)(1-A)/C Table 1 When analyzing an optical system, we often are first interested in basic properties of the system such as the focal length (or optical power of the system) and the location of the focal planes, etc. In the limit of paraxial optics, any optical system, from a simple lens to a combination of lenses, mirrors and ducts, can be described in terms of six special surfaces, called the cardinal surfaces of the system. In paraxial optics, these surfaces are planes, normal to the optical axis. The point where the plane intersects the optical axis is the cardinal point corresponding to that cardinal plane. The six special planes are: First Focal Plane Second Focal Plane First Principle Plane Second Principle Plane First Nodal Plane Second Nodal Plane Once we know the location of these special planes, relative to the physical location of the lenses in the system, we can describe all of the paraxial imaging properties of the system. -
How Do the Lenses in a Microscope Work?
Student Name: _____________________________ Date: _________________ How do the lenses in a microscope work? Compound Light Microscope: A compound light microscope uses light to transmit an image to your eye. Compound deals with the microscope having more than one lens. Microscope is the combination of two words; "micro" meaning small and "scope" meaning view. Early microscopes, like Leeuwenhoek's, were called simple because they only had one lens. Simple scopes work like magnifying glasses that you have seen and/or used. These early microscopes had limitations to the amount of magnification no matter how they were constructed. The creation of the compound microscope by the Janssens helped to advance the field of microbiology light years ahead of where it had been only just a few years earlier. The Janssens added a second lens to magnify the image of the primary (or first) lens. Simple light microscopes of the past could magnify an object to 266X as in the case of Leeuwenhoek's microscope. Modern compound light microscopes, under optimal conditions, can magnify an object from 1000X to 2000X (times) the specimens original diameter. "The Compound Light Microscope." The Compound Light Microscope. Web. 16 Feb. 2017. http://www.cas.miamioh.edu/mbi-ws/microscopes/compoundscope.html Text is available under the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) license. - 1 – Student Name: _____________________________ Date: _________________ Now we will describe how a microscope works in somewhat more detail. The first lens of a microscope is the one closest to the object being examined and, for this reason, is called the objective. -
Laboratory 7: Properties of Lenses and Mirrors
Laboratory 7: Properties of Lenses and Mirrors Converging and Diverging Lens Focal Lengths: A converging lens is thicker at the center than at the periphery and light from an object at infinity passes through the lens and converges to a real image at the focal point on the other side of the lens. A diverging lens is thinner at the center than at the periphery and light from an object at infinity appears to diverge from a virtual focus point on the same side of the lens as the object. The principal axis of a lens is a line drawn through the center of the lens perpendicular to the face of the lens. The principal focus is a point on the principal axis through which incident rays parallel to the principal axis pass, or appear to pass, after refraction by the lens. There are principle focus points on either side of the lens equidistant from the center (See Figure 1a). Figure 1a: Converging Lens, f>0 Figure 1b: Diverging Lens, f<0 In Fig. 1 the object and image are represented by arrows. Two rays are drawn from the top of the object. One ray is parallel to the principal axis which bends at the lens to pass through the principle focus. The second ray passes through the center of the lens and undeflected. The intersection of these two rays determines the image position. The focal length, f, of a lens is the distance from the optical center of the lens to the principal focus. It is positive for a converging lens, negative for a diverging lens. -
Lecture 37: Lenses and Mirrors
Lecture 37: Lenses and mirrors • Spherical lenses: converging, diverging • Plane mirrors • Spherical mirrors: concave, convex The animated ray diagrams were created by Dr. Alan Pringle. Terms and sign conventions for lenses and mirrors • object distance s, positive • image distance s’ , • positive if image is on side of outgoing light, i.e. same side of mirror, opposite side of lens: real image • s’ negative if image is on same side of lens/behind mirror: virtual image • focal length f positive for concave mirror and converging lens negative for convex mirror and diverging lens • object height h, positive • image height h’ positive if the image is upright negative if image is inverted • magnification m= h’/h , positive if upright, negative if inverted Lens equation 1 1 1 푠′ ℎ′ + = 푚 = − = magnification 푠 푠′ 푓 푠 ℎ 푓푠 푠′ = 푠 − 푓 Converging and diverging lenses f f F F Rays refract towards optical axis Rays refract away from optical axis thicker in the thinner in the center center • there are focal points on both sides of each lens • focal length f on both sides is the same Ray diagram for converging lens Ray 1 is parallel to the axis and refracts through F. Ray 2 passes through F’ before refracting parallel to the axis. Ray 3 passes straight through the center of the lens. F I O F’ object between f and 2f: image is real, inverted, enlarged object outside of 2f: image is real, inverted, reduced object inside of f: image is virtual, upright, enlarged Ray diagram for diverging lens Ray 1 is parallel to the axis and refracts as if from F. -
Shedding Light on Lenses
Shedding Light on Lenses Teachers’ Notes Shedding Light on Lenses (56 minutes) is the fifth video in the phenomenal Shedding Light series of videos. Conveniently broken up into nine sections, Science teacher Spiro Liacos uses fantastic visuals and animations to explain how convex and concave lenses produce images in a wide variety of situations. After a quick recap on refraction, Spiro illustrates how magnifying glasses work and how projectors produce giant images on giant cinema screens. He then looks into, quite literally, a tuna fish’s eye to show how our eyes work. After explaining how concave lenses produce images, he discusses how spectacles help people who have vision defects. The first bonus feature takes a fun look at slow motion, fast motion and stop motion, and the second bonus feature, aimed at more advanced students, covers the mathematics of lenses and image formation. The program comes with fantastic activity sheets which will help students to learn the content and to develop new skills in drawing ray diagrams. Part A: An Introduction to Lenses A brief recap of refraction and an introduction to convex and concave lenses. Part B: Convex Lenses Convex lenses focus light rays inwards. They can be used to start a fire and are used in so-called projector headlights. Part C: Images Produced by Convex Lenses (when the object is close to the lens) Magnifying glasses, ray diagrams and reference rays… Part D: Images Produced by Convex Lenses (when the object is further than the focal length of the lens) Slide projectors, film projectors and electronic DLP projectors are the contexts in which the concept of a “real image” is demonstrated to students. -
1.0 Measurement of Paraxial Properties of Optical Systems
1.0 MEASUREMENT OF PARAXIAL PROPERTIES OF OPTICAL SYSTEMS James C. Wyant Optical Sciences Center University of Arizona Tucson, AZ 85721 [email protected] If we wish to completely characterize the paraxial properties of a lens, it is necessary to measure the exact location of its cardinal points, that is, its nodal points, focal points, and principal points. For a lens in air the nodal points and principal points coincide. For a thin lens, the two principal points coincide at the center of the lens, so the only required measurement is the focal length, while for a thick lens two of the three quantities--focal length, two focal points, or two principal points--must be determined. 1.1 Thin Lenses 1.1.1 Measurements Based on Image Equation The simplest measurements of the focal length of a thin lens are based on the image equation 1 1 1 + = (1.1) p q f where p is the object distance from the lens (positive if the object is before the lens), q is the image distance from the lens (positive if the image is after the lens), and f is the focal length of the lens. If the lens to be tested has a positive power, a real image can be formed of a pinhole source, and the distances p and q can be measured directly. When the lens to be tested has a negative power, it should be combined with a positive auxiliary lens having sufficient power so that the combination forms a real image. The focal length can then be determine for the auxiliary lens alone and the combination of lenses. -
Optics Course (Phys 311)
Optics Course (Phys 311) Geometrical Optics Refraction through Lenses Lecturer: Dr Zeina Hashim Phys Geometrical Optics: Refraction (Lenses) Lesson 2 of 2 311 Slide 1 Objectives covered in this lesson : 1. The refracting power of a thin lens. 2. Thin lens combinations. 3. Refraction through thick lenses. Phys Geometrical Optics: Refraction (Lenses) Lesson 2 of 2 311 Slide 2 The Refracting Power of a Thin Lens: The refracting power of a thin lens is given by: 1 푃 = 푓 Vergence: is the convergence or divergence of rays: 1 1 푉 = and 푉′ = 푝 푖 ∴ 푉 + 푉′ = 푃 A diopter (D): is a unit used to express the power of a spectacle lens, equal to the reciprocal of the focal length in meters. Phys Geometrical Optics: Refraction (Lenses) Lesson 2 of 2 311 Slide 3 The Refracting Power of a Thin Lens: Individual Activity Q: What is the refracting power of a lens in diopters if the lens has a focal length = 20 cm ? Phys Geometrical Optics: Refraction (Lenses) Lesson 2 of 2 311 Slide 4 Thin Lens Combinations: If the optical system is composed of more than one lens (or a combination of lenses and mirrors) which are located so that their optical axes coincide: the final image can be obtained by working in steps: 1. Consider the nearest lens only, find the image of the object through this lens. 2. The image in step 1 is the object for the second (adjacent) optical component: find the image of this object. This can be done both geometrically or numerically 3. -
11.4 the Optics of Other Devices
11.4 The Optics of Other Devices projection head Activity 11.4.1 Optics of an Overhead Projector focus knob Overhead projectors (Figure 1), like many optical systems, consist of three sys- tems that work together: a mechanical system, an electronic system, and an optical system. Their function is to project an enlarged image from a transparent film onto a distant screen. In this activity, you will see how the different optical optical components of the projector work together. stage Materials overhead projector appropriate screwdrivers projector case Procedure Figure 1 1. Before turning on the overhead projector, open the optical stage to see An overhead projector inside the projector case. Sketch the arrangement of optical components by considering what a cross-section of the projector would look like. Note the arrangement of any bulbs, mirrors, or lenses that you find in the projector case. Add the optics of the projection head to your sketch. 2. Turn on the projector to project an image of a letter onto a screen nearby. Make adjustments to focus the image. 3. Use the focus knob to move the projection head upward. How does this affect the image? Refocus the image. 4. Use the focus knob to move the projection head downward. How does this affect the image? Refocus the image. 5. Move the projector farther from the screen. How does this affect the image? Analysis (a) Draw a ray diagram, with at least three different rays, showing how light travels from the bulb to the screen. (b) In table form, describe the structure and function of each optical compo- nent of the overhead projector. -
Geometric Optics
GEOMETRIC OPTICS I. What is GEOMTERIC OPTICS In geometric optics, LIGHT is treated as imaginary rays. How these rays interact with at the interface of different media, including lenses and mirrors, is analyzed. LENSES refract light, so we need to know how light bends when entering and exiting a lens and how that interaction forms an image. MIRRORS reflect light, so we need to know how light bounces off of surfaces and how that interaction forms an image. II. Refraction We already learned that waves passing from one media to another cause light to do two things: Change path Change wavelength which means…Change velocity (speed of light) The velocity DECREASES and the wavelength SHORTENS when light passes from a “faster” to a “slower” media. The velocity INCREASES and the wavelength LENGTHENS when light passes from a “slower” to a “faster” media. In either case, the FREQUENCY remains the same. 1 refraction, continued When light hits the interface of two media at an angle, the lower part of the ray interacts first, thus slowing it down before the rest of the ray meets the interface. This rotates the ray toward the normal. The NORMAL LINE is an imaginary line PERPENDICULAR to the interface of two media. The REFRACTIVE INDEX of a substance tells you how much light will change speed (or bend) when it passes through the substance. It is the ratio of the speed of light in the medium to the speed of light in a vacuum. The medium will commonly n is the refractive index be air, water, glass, plastic c is the speed of light in a vacuum 2 refraction, continued substance refractive index, n vacuum 1 air 1.000277 water 1.333 glass 1.50 The table of refractive index values shows you that light slows down only a little in air, but its speed is reduced about 33% in glass.