# INTRODUCTION THIN LENSES. Introduction. given by the paraxial refraction equation derived last lecture: Thin lenses (19.1) = 1. Double-lens systems

Save this PDF as:

Size: px
Start display at page:

Download "INTRODUCTION THIN LENSES. Introduction. given by the paraxial refraction equation derived last lecture: Thin lenses (19.1) = 1. Double-lens systems"

## Transcription

1 Chapter 9 OPTICAL INSTRUMENTS Introduction Thin lenses Double-lens systems Aberrations Camera Human eye Compound microscope Summary INTRODUCTION Knowledge of geometrical optics, diffraction and interference, allows calculation of the operation and performance of instruments that focus electromagnetic waves. There are many applications to both optical and non optical instruments. This discussion will be limited to three optical systems that are most frequently encountered in the medical field, namely, the camera, the human eye, and the microscope. These illustrate the general features of optics. First it is necessary to complete the discussion of the optics of thin lens systems. Converging thin lens THIN LENSES Consider two refracting convex spherical surfaces as shown in figure. Assume that the object and image are in air with refractive index unity, while the glass lens has refractive index n. At the first surface the image distance is drawn for the case where it is negative. At the first surface the object and image distance are given by the paraxial refraction equation derived last lecture: = (9.) The image of surface serves as the object for surface 2 with object distance 2 = + where is the distance separating the two surfaces. Thus for the second surface we have a paraxial refraction equation: + + = 2 2 The geometry for this pair of refracting surfaces is simplified if the thin lens approximation is assumed that is, =0Then this last refraction equation equals: + = (9.2) 2 2 Combining the paraxial refraction equations for each surface gives: + µ =( ) 2 2 (Thin-lens approximation) Define the focal length as: µ =( ) (Lens-makers equation) 2 Thus the thin lens equation can be written as: + = (Thin-lens equation.) where the subscripts and 2 are dropped. The adopted sign convention has positive on the incident (left-hand) side, positive on the transmission (right-hand) side, and positive for a converging thin lens and negative for a diverging thin lens. Note that if either or are infinite, then the other distance equals the focal length. That is, a parallel ray focusses at the focal point a distance from the lens. Figure 2 shows the focal points for converging and diverging lenses. The power ofalensisdefined as: = (Power of a lens) The unit of lens power is the diopter which is the value of when the focal length is given in meters. Thus a +0 diopter lens is a converging lens with focal length 0, whilea 0 diopter lens is a diverging lens of focal length 0. From figure 3 it is obvious by proportion that the magnification for a converging lens is given by: Figure lens. Refraction at two spherical surfaces of a glass = = (Magnification) 4

2 Figure 2 Focal points for converging (a) and diverging (b) lenses. Figure 4 Image for a converging lens of focal length =333 for (a) =20, and(b) =0. Figure 3 Magnification for a converging lens. Figure 5 A diverging lens system. Example of converging lens Consider the glass has =5, and the lens surfaces have = 0 and 2 = 20 Then using the lens-makers equation we have; = µ =(5 0) 00 =75 diopters 020 Thatis,thefocallengthis =333. Considerthecaseof =20 shown in figure 4a, then substitution in the lens formula gives: 02 + =75 that is, =40 For this case the magnification is = 20 that is the image is inverted. Considerthecasewhere =0 shown in figure 4b, then substitution in the lens formula gives = 40 and magnification =+40that is the image now is erect, not inverted. Example of diverging lens For the diverging lens shown in figure 5, we have a power given by: = µ =(5 0) 05 = that is the focal length is = 2 If the object is at =20 then the thin lens formula gives the image at I where: 02 + = 8333 Thus = 75, that is the image is virtual. The magnification is =+0375that is the image is erect not inverted. DOUBLE-LENS SYSTEMS For multiple lens systems, the final image is found by calculating the image from the first lens and then using this image as the object for the next lens to calculate the second image. This process can be repeated for a series of lenses. Let us consider double-lens systems. Twoconverginglenses The microscope, telescope, magnifying lens, and the use of reading glasses all are examples where one has systems of two converging lenses. For the system shown in figure 6, the thin-lens formula for the first lens of focal length gives: = (Lens ) because is negative. Using the image of lens as the object of lens 2, and taking into account the separation 42

3 Figure 6 Double-lens system d between the lenses, gives: ( + ) + = (Lens 2) 2 2 Using these two equations allows calculation of the final image. Moreover, the total magnification of the system is the product of the separate magnifications: = 2 Note the special case when the separation between thelensesiszero, =0Then adding the two lens equations gives: + = That is, the power of a compound pair of lenses with zero separation is Figure 7 Barrel distortion for a wide angle lens. = + 2 (Compound lenses with zero separation) Thus the powers are additive if the separation between the lenses is zero. Contact lenses are an example of compound lenses with essentially zero separation between the lens. The eye needs to have an effective power of about 50 diopters to focus far objects on the retina. For the myopic, short-sighted, eye the power of the lens in the eye is too powerful so a diverging lens with negative power, e.g. 0 diopters, is used to reduce the power of the compound system. For the long-sighted eye, the eye lens is not powerful enough so a converging lens, with positive power, is used to increase the power of the compound system. ABERRATIONS The lens and mirror equations were derived assuming the paraxial approximation, that is, all angles are small enough to assume that sin = This breaks down if the radius of the lens or mirror is large compared with the object or image distances, or if the object is far from the axis of the lens system. When the smallangle approximation fails, the rays through different parts of the lens do not focus at the same point giving a blurred image. Spherical aberration is due the Figure 8 Chromatic aberration is the different focal lengths for different frequencies due to the variation of refractive index on frequency. break down caused by the size of the lens while barrel or pin-cushion distortion is due to large diplacement of theobjectfromtheaxisofthelens. Comaandastigmatism are combinations of these two effects. Barrel distortion is observed when using a wide-angle camera lens as shown in figure 7. Chromatic aberration is caused by the fact that the refractive index is frequency dependent. Thus the focal length of a thin lens is frequency dependent causing different colors to focus at different image distances as shown in figure 8. It is possible to make a compound lens of two types of glass that have different dependences of refractive index on frequency. With such an achromatic doublet, illustrated in figure 9, it is possible to arrange that the focal length is the same at two frequencies. Note that chromatic aberration is not a problem for reflective imaging systems. 43

4 Figure 9 Achromatic doublet. be assumed that ' The performance of the camera can be broken into five main elements; lens speed, shutter speed, resolution, depth of focus, and field of view. Camera design is a compromise between the conflicting requirements of these five aspects. Lens speed The light flux collected by the camera lens is proportional to the area of the lens aperture, that is 2 4 Since the image size is proportional to, then the image area is proportional to 2 Thus the power ³ 2 density of the image is Define the Fnumberof the lens, as = (F-number of a lens.) Thus the image power density is: Figure 0 The main elements of a camera. CAMERA The camera is a relatively simple optical system and yet it demonstrates the many compromises that must be made is design and use of optical systems. Figure 0 shows a schematic of the main elements of the camera. The lens is shown in figure is an achromatic doublet to correct for chromatic aberration. Most camera lens comprise several lenses to minimize aberrations in order to obtain a good resolution with a wide field of view. The iris of the lens has an aperture of diameter D. The object distance normally is thus the image distance is For example, a typical 35mm camera lens has a focal length of =50. Thus =50 for = and =53 when =2 Therefore in the subsequent discussion it will Image power density 2 The brightness of the final image is proportional to the energy density which is the power density times the time the shutter is open. Note that for an expensive camera lens =22 is the smallest aperture and =0 the largest aperture. The ratio of image power densities is almost 500 for these extreme cases. Moreover, one can vary the shutter speed by a factor of 0 3 increasing the dynamic range of usable light intensity to nearly 0 6 Shutter speed Clearly, the shutter speed must be sufficiently small to ensure that the image does not move significantly while the shutter is open. Unfortunately, the shorter the shutter speed, the less light that is collected. A fast film, and small F number are required to compensate for use of a fast shutter speed. Resolution There are two limits to resolution, diffraction and granularity of the film emulsion or the CCD digital sensor. Diffraction sets an angular resolution of =22 For an image distance of = this gives the spatial width between the first minima as: =244 (Diffraction spatial resolution.) Figure The optics of a camera. This implies that the best diffraction resolution is obtained with small F numbers. Typically, for = 500the spatial resolution is =22. The emulsion of a slow fine-grain film has a resolution of about 0 which limits the resolution in a 35mm camera for 0 Faster speed films, that is, those with a higher ASA number have poorer spatial 44

5 Figure 2 Diffraction spatial width. Figure 4 Illustration of the depth of focus of a camera. Figure 3 Depth of focus resolution. Digital cameras have a poorer resolution due to the limited number of pixels used to record the picture, that is, spatial resolution of 35 for a typical camera. Depth of focus Onewouldliketohavebothnearandfarobjectsin focus. As shown in figure 3, relocating the object relocates the image resulting in an out-of-focus blurr of diameter on the emulsion. Since + = then = 2 Thus the width of the blurr on the emulsion 2 is given by: That is: = = 2 2 = 2 2 (Depth of focus) Considera35mmcamerawith =5, =25 and let the blurr width equal the emulsion resolution =0 5. These give a depth of focus for an object at =, of =!. That is, the depth of focus is only one centimeter, which is half the depth of your nose. To achieve good depth of focus one needs to use a very large F number, such as a pinhole camera. Figure 4 shows an example of deph of focus. Field of view An f=50mm focal length lens, on a 35mm camera, has about the field of view of the eye. A smaller focal length is required to obtain a wider field of view for a Figure 5 The human eye given size sensor. However, such a smaller focal length implies a smaller image for which film graininess will be more important. The wider field of view makes lens aberrations more noticeable. Barrel distortion is a typical problem using very wide-angle lenses. It is not possible to simultaneously satisfy the conflicting requirements of lens speed, shutter speed, resolution, depth of focus and field of view. The camera parameters are adjusted by each photographer to achieve his or her balance of these conflicting requirements for each picture. HUMAN EYE The optics of the human eye is effectively the same as that of the camera, and thus we can use the equations developed for the camera. The components of the eye are shown in figure 5. The focal length of the eye is 20, the iris ranges from =5 to 6, and thusthefnumberrangesfrom3to3whichisquite modest compared with a typical camera. The cones on the retina are clustered around the central region of view and have a spatial resolution of 45

6 Figure 7 Figure 6 Wavelength sensitivity of rods and cones of the human eye. 0 6 The cones are surrounded by the rods which have a resolution of Thus the cones have an angular resolution of 02 minutes of arc while the rods have an angular resolution of 06 minutes of arc. Diffraction at the pupil of the eye limits the resolution to about which is a good balance with the resolution of the rods and cones in the retina. Note that the moon and sun both subtend about 33 minutes of arc at the earth, thus the best angular resolution achievable by the eye is the order of 06% of the angular size of the moon. The F number of the eye only changes by a factor of 4, so the speed of the lens only changes by a factor of 6 due to opening of the iris. However, in the dark the eye sensitivity increases by a factor of 5000 over a period of 5 hours. This behavior is observed when you walk into a darkened room from bright daylight, initially you cannot see objects that are clearly visible by the dark-adapted eye. The explanation is that the cones, which have an excellent spatial resolution and color sensitivity, have low light sensitivity. However, the rods have high light sensitivity, lower spatial resolution and are insensitive to red light. Figure 6 compares the wavelength response of the cones and rods. The rods are saturated in bright light and their light sensitivity gradually recovers in the dark. Note the the peripheral vision of the eye, which focusses on the rods, is the most sensitive at low light levels, but it does not see red. Thus highest sensitivity is achieved by looking slightly to the side of an object at night rather than staring directly at it. Red light is used in aircraft cockpits to ensure that the eye remain dark adapted at night. The power of the eyeball lens decreases with age resulting in a steady increase in the near point as shown in figure 7. As a result it is necessary to use reading glasses which comprise converging lenses which produce a virtual image at the near point of the eye allowing one to focus as shown in figure 8. Myopia is the opposite effect where the focal length of the eye is too small resulting in an image in front of Figure 8 The use of a converging lens produces an enlarged virtual image that can be seen by the hyperopic eye. the retina. A negative power lens is required to weaken the power of the eye lens as shown in figure 9 COMPOUND MICROSCOPE The compound microscope is shown in figure 20. The objective forms an enlarged, inverted, real image of the object. This image is at a distance L, called the tube length, from the near focal point. Figure 9 The myopic eye has too short a focal length lens. A negative power corrective lens is required to focus the image on the retina. 46

7 Figure 20 Magnification The compound microscope. The lateral magnification by the objective is = (Objective magnification) The normal eye can focus objects at object distance from 25 to The image on the retina of the eye is largest when the object is closest, that is at the near point. A magnifying lens produces an image at the near point of the eye, of an object that is very close to the eye. Since the object of a magnifying glass is close to the eye it subtends a large angle leading to a large image on the retina of the eye. Since the focal lens of a microscope eyepiece is much smaller than 25, the object distance for the eyepiece almost equals the focal length of the eyepiece, producing a virtual noninverted image at 25. Thus the magnification of the eyepiece is (near point) = (Eyepiece magnification) The net magnification is the product of the objective and eyepiece magnifications. As an example consider a typical microscope with = 5, tube length = 20 eyepiece focal length = 2 and taking the near point at 25 cm. Then the objective has a magnification of = = 40 and the eyepiece magnification is = 25 2 =+25 Thus the microscope has a net transverse magnification of = 500. Resolution The discussion of diffraction pointed out that for a circular aperture the angle of the first minimum of a diffraction pattern occurs at sin min =22 where is the diameter of the circular object being imaged. Note that is not the diameter of the objective, it is the diameter of the circular object being magnified. The information about the fine structure of the Figure 2 Light collection of diffraction pattern by objective lens. object is carried by the diffraction pattern. To obtain a perfect image one must collect all the diffracted light. If the lens has a maximum acceptance angle then even the first minimum will not be accepted by 22 sin the lens for aperture widths less than = That is, there is a minimum spacing for which the lens will accept enough of the diffraction pattern to carry the information as to the spatial dimension. That is, the smallest spatial resolution min is given by: min = 22 sin (Spatial resolution of dry objective lens.) Assuming that the objective collects light to 65 to the normal, that is a maximum value of the numerical aperture sin =09 then diffraction sets a minimum resolved structure, for = 500 to be = 680 Ifthevolumebetweentheobjectandobjectivelens is filled with an oil of refractive index n, then the wavelength in the oil is = Since the refractive index exceeds unity, then the wavelength in oil is less than is vacuum. The above discussion about resolution is modified in that the wavelength of interest is the one in oil. Thus we get for an oil immersion objective, that 22 min = sin (Spatial resolution for an oil immersion objective lens.) Good oil immersion objective have a numerical aperture = sin =4. Such a lens will give a spatial resolution of 480nm. It is not possible to attain better spatial resolution using = 500 light. Shorter wavelength light is required. As will be discussed later, much shorter wavelengths, such as X rays or electron matter waves, are needed to attain spatial resolutions of 0 0 which istheorderofthesizeoftheatom. Modernintegrated circuit manufacture uses UV light to be able to make the 0.80 micron size traces on silican wafers. 47

8 Figure 22 The phase-contrast microscope restricts the angular range of the incident light through the condenser lens. After the light passes through the objective of the microscope the phase of the unscattered light, shown red, is retarded by 90 by a phase plate. This results in thesmallphasedifference in the scattered light shown in yellow, which is not easily visible by eye, being converted to differences in amplitude of the combined light which greatly enhances the visibility of thin biological samples. Figure 23 Comparison of the observed light scattered by a thin biological sample using a conventional microscope, shownontheleft,withthatfromaphase-contrast microscope, shown on the right. SUMMARY The performance of optical instruments is a compromise between several contradictory requirements due to geometrical optics and wave properties. Reading assignment: Giancoli, Chapter 34. Phase-contrast microscopy. One problem with biological samples is that thin slices tend to be transparent and thus little contrast is seen between different parts of the sample. Phase contrast microscopy uses a trick to change the phase between the primary and secondary diffraction maxima resulting in phase differences shown as differing image brightness. As shown in figure 22, an annular slit restricts the angular range of the light focussed by the condenser lens onto the object, shown in green. Most of the light is unscattered by the specimen, shown in red. The diffracted light, shown in yellow, contains the required spatial information regarding the specimen. Unfortunately the weak diffracted light is shifted in phase by 90 andthusasshownthenetvector,shown in blue, is essentially the same as the unscattered direct light, shown in red. That is, the length of the red and blue vectors are essentially the same. The eye is only sensitive to the intensity of the light, not the phase. The trick is to retard the phase of the central (red) unscattered light by 90 by use of a phase shift ring behind the objective. The sum of the in-phase red and yellow vectors resulting in a change in the intensity shown in blue. A further trick is to attenuate the strong unscattered light by use of a grey filter ring which enhances the ratio of the yellow and attenuated red intensities. Thus, variations in refractive index across a sample, which corresponds to phase differences, are displayed as differences in contrast. Figure 23 illustrates that the phase differences, shown on the left, become much more clearly defined by the phaseshift microscope as seen by the eye which is sensitive to differences in contrast, not phase differences. 48

### OPTICAL SYSTEMS OBJECTIVES

101 L7 OPTICAL SYSTEMS OBJECTIVES Aims Your aim here should be to acquire a working knowledge of the basic components of optical systems and understand their purpose, function and limitations in terms

### Lecture Outline Chapter 27. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc.

Lecture Outline Chapter 27 Physics, 4 th Edition James S. Walker Chapter 27 Optical Instruments Units of Chapter 27 The Human Eye and the Camera Lenses in Combination and Corrective Optics The Magnifying

### Lecture PowerPoint. Chapter 25 Physics: Principles with Applications, 6 th edition Giancoli

Lecture PowerPoint Chapter 25 Physics: Principles with Applications, 6 th edition Giancoli 2005 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for the

### VISUAL PHYSICS ONLINE DEPTH STUDY: ELECTRON MICROSCOPES

VISUAL PHYSICS ONLINE DEPTH STUDY: ELECTRON MICROSCOPES Shortly after the experimental confirmation of the wave properties of the electron, it was suggested that the electron could be used to examine objects

### There is a range of distances over which objects will be in focus; this is called the depth of field of the lens. Objects closer or farther are

Chapter 25 Optical Instruments Some Topics in Chapter 25 Cameras The Human Eye; Corrective Lenses Magnifying Glass Telescopes Compound Microscope Aberrations of Lenses and Mirrors Limits of Resolution

### Chapter 34 Geometric Optics (also known as Ray Optics) by C.-R. Hu

Chapter 34 Geometric Optics (also known as Ray Optics) by C.-R. Hu 1. Principles of image formation by mirrors (1a) When all length scales of objects, gaps, and holes are much larger than the wavelength

### Chapter 29/30. Wave Fronts and Rays. Refraction of Sound. Dispersion in a Prism. Index of Refraction. Refraction and Lenses

Chapter 29/30 Refraction and Lenses Refraction Refraction the bending of waves as they pass from one medium into another. Caused by a change in the average speed of light. Analogy A car that drives off

### Chapter 18 Optical Elements

Chapter 18 Optical Elements GOALS When you have mastered the content of this chapter, you will be able to achieve the following goals: Definitions Define each of the following terms and use it in an operational

### Chapter 34: Geometrical Optics (Part 2)

Chapter 34: Geometrical Optics (Part 2) Brief review Optical instruments Camera Human eye Magnifying glass Telescope Microscope Optical Aberrations Phys Phys 2435: 22: Chap. 34, 31, Pg 1 The Lens Equation

### Image Formation. Light from distant things. Geometrical optics. Pinhole camera. Chapter 36

Light from distant things Chapter 36 We learn about a distant thing from the light it generates or redirects. The lenses in our eyes create images of objects our brains can process. This chapter concerns

### Converging and Diverging Surfaces. Lenses. Converging Surface

Lenses Sandy Skoglund 2 Converging and Diverging s AIR Converging If the surface is convex, it is a converging surface in the sense that the parallel rays bend toward each other after passing through the

### Geometrical Optics Optical systems

Phys 322 Lecture 16 Chapter 5 Geometrical Optics Optical systems Magnifying glass Purpose: enlarge a nearby object by increasing its image size on retina Requirements: Image should not be inverted Image

### Astronomy 80 B: Light. Lecture 9: curved mirrors, lenses, aberrations 29 April 2003 Jerry Nelson

Astronomy 80 B: Light Lecture 9: curved mirrors, lenses, aberrations 29 April 2003 Jerry Nelson Sensitive Countries LLNL field trip 2003 April 29 80B-Light 2 Topics for Today Optical illusion Reflections

### Introduction to Light Microscopy. (Image: T. Wittman, Scripps)

Introduction to Light Microscopy (Image: T. Wittman, Scripps) The Light Microscope Four centuries of history Vibrant current development One of the most widely used research tools A. Khodjakov et al. Major

### Chapter 34 Geometric Optics

Chapter 34 Geometric Optics Lecture by Dr. Hebin Li Goals of Chapter 34 To see how plane and curved mirrors form images To learn how lenses form images To understand how a simple image system works Reflection

### Lenses. A lens is any glass, plastic or transparent refractive medium with two opposite faces, and at least one of the faces must be curved.

PHYSICS NOTES ON A lens is any glass, plastic or transparent refractive medium with two opposite faces, and at least one of the faces must be curved. Types of There are two types of basic lenses. (1.)

### Chapter 2 - Geometric Optics

David J. Starling Penn State Hazleton PHYS 214 The human eye is a visual system that collects light and forms an image on the retina. The human eye is a visual system that collects light and forms an image

### Lenses. Images. Difference between Real and Virtual Images

Linear Magnification (m) This is the factor by which the size of the object has been magnified by the lens in a direction which is perpendicular to the axis of the lens. Linear magnification can be calculated

### University of Rochester Department of Physics and Astronomy Physics123, Spring Homework 5 - Solutions

Problem 5. University of Rochester Department of Physics and Astronomy Physics23, Spring 202 Homework 5 - Solutions An optometrist finds that a farsighted person has a near point at 25 cm. a) If the eye

### c v n = n r Sin n c = n i Refraction of Light Index of Refraction Snell s Law or Refraction Example Problem Total Internal Reflection Optics

Refraction is the bending of the path of a light wave as it passes from one material into another material. Refraction occurs at the boundary and is caused by a change in the speed of the light wave upon

### Chapter 34: Geometric Optics

Chapter 34: Geometric Optics It is all about images How we can make different kinds of images using optical devices Optical device example: mirror, a piece of glass, telescope, microscope, kaleidoscope,

### Person s Optics Test KEY SSSS

Person s Optics Test KEY SSSS 2017-18 Competitors Names: School Name: All questions are worth one point unless otherwise stated. Show ALL WORK or you may not receive credit. Include correct units whenever

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A plane mirror is placed on the level bottom of a swimming pool that holds water (n =

### SUBJECT: PHYSICS. Use and Succeed.

SUBJECT: PHYSICS I hope this collection of questions will help to test your preparation level and useful to recall the concepts in different areas of all the chapters. Use and Succeed. Navaneethakrishnan.V

### Chapter 23. Mirrors and Lenses

Chapter 23 Mirrors and Lenses Mirrors and Lenses The development of mirrors and lenses aided the progress of science. It led to the microscopes and telescopes. Allowed the study of objects from microbes

### Mirrors, Lenses &Imaging Systems

Mirrors, Lenses &Imaging Systems We describe the path of light as straight-line rays And light rays from a very distant point arrive parallel 145 Phys 24.1 Mirrors Standing away from a plane mirror shows

### Chapter 23. Light Geometric Optics

Chapter 23. Light Geometric Optics There are 3 basic ways to gather light and focus it to make an image. Pinhole - Simple geometry Mirror - Reflection Lens - Refraction Pinhole Camera Image Formation (the

### CHAPTER 34. Optical Images

CHAPTER 34 1* Can a virtual image be photographed? Yes. Note that a virtual image is seen because the eye focuses the diverging rays to form a real image on the retina. Similarly, the camera lens can focus

Chapter 34 Images Copyright 34-1 Images and Plane Mirrors Learning Objectives 34.01 Distinguish virtual images from real images. 34.02 Explain the common roadway mirage. 34.03 Sketch a ray diagram for

### Waves & Oscillations

Physics 42200 Waves & Oscillations Lecture 27 Geometric Optics Spring 205 Semester Matthew Jones Sign Conventions > + = Convex surface: is positive for objects on the incident-light side is positive for

### Chapter 26. The Refraction of Light: Lenses and Optical Instruments

Chapter 26 The Refraction of Light: Lenses and Optical Instruments 26.1 The Index of Refraction Light travels through a vacuum at a speed c=3. 00 10 8 m/ s Light travels through materials at a speed less

### CHAPTER 18 REFRACTION & LENSES

Physics Approximate Timeline Students are expected to keep up with class work when absent. CHAPTER 18 REFRACTION & LENSES Day Plans for the day Assignments for the day 1 18.1 Refraction of Light o Snell

### Dr. Todd Satogata (ODU/Jefferson Lab) Monday, April

University Physics 227N/232N Mirrors and Lenses Homework Optics 2 due Friday AM Quiz Friday Optional review session next Monday (Apr 28) Bring Homework Notebooks to Final for Grading Dr. Todd Satogata

### Vision. The eye. Image formation. Eye defects & corrective lenses. Visual acuity. Colour vision. Lecture 3.5

Lecture 3.5 Vision The eye Image formation Eye defects & corrective lenses Visual acuity Colour vision Vision http://www.wired.com/wiredscience/2009/04/schizoillusion/ Perception of light--- eye-brain

### Name. Light Chapter Summary Cont d. Refraction

Page 1 of 17 Physics Week 12(Sem. 2) Name Light Chapter Summary Cont d with a smaller index of refraction to a material with a larger index of refraction, the light refracts towards the normal line. Also,

### Astronomical Cameras

Astronomical Cameras I. The Pinhole Camera Pinhole Camera (or Camera Obscura) Whenever light passes through a small hole or aperture it creates an image opposite the hole This is an effect wherever apertures

### Geometric Optics. Ray Model. assume light travels in straight line uses rays to understand and predict reflection & refraction

Geometric Optics Ray Model assume light travels in straight line uses rays to understand and predict reflection & refraction General Physics 2 Geometric Optics 1 Reflection Law of reflection the angle

### PHY 431 Homework Set #5 Due Nov. 20 at the start of class

PHY 431 Homework Set #5 Due Nov. 0 at the start of class 1) Newton s rings (10%) The radius of curvature of the convex surface of a plano-convex lens is 30 cm. The lens is placed with its convex side down

### Chapter 23. Mirrors and Lenses

Chapter 23 Mirrors and Lenses Notation for Mirrors and Lenses The object distance is the distance from the object to the mirror or lens Denoted by p The image distance is the distance from the image to

### PHYSICS 289 Experiment 8 Fall Geometric Optics II Thin Lenses

PHYSICS 289 Experiment 8 Fall 2005 Geometric Optics II Thin Lenses Please look at the chapter on lenses in your text before this lab experiment. Please submit a short lab report which includes answers

### Chapter 3 Optical Systems

Chapter 3 Optical Systems The Human Eye [Reading Assignment, Hecht 5.7.1-5.7.3; see also Smith Chapter 5] retina aqueous vitreous fovea-macula cornea lens blind spot optic nerve iris cornea f b aqueous

### Lecture 17. Image formation Ray tracing Calculation. Lenses Convex Concave. Mirrors Convex Concave. Optical instruments

Lecture 17. Image formation Ray tracing Calculation Lenses Convex Concave Mirrors Convex Concave Optical instruments Image formation Laws of refraction and reflection can be used to explain how lenses

### Test Review # 8. Physics R: Form TR8.17A. Primary colors of light

Physics R: Form TR8.17A TEST 8 REVIEW Name Date Period Test Review # 8 Light and Color. Color comes from light, an electromagnetic wave that travels in straight lines in all directions from a light source

### Refraction, Lenses, and Prisms

CHAPTER 16 14 SECTION Sound and Light Refraction, Lenses, and Prisms KEY IDEAS As you read this section, keep these questions in mind: What happens to light when it passes from one medium to another? How

### CH. 23 Mirrors and Lenses HW# 6, 7, 9, 11, 13, 21, 25, 31, 33, 35

CH. 23 Mirrors and Lenses HW# 6, 7, 9, 11, 13, 21, 25, 31, 33, 35 Mirrors Rays of light reflect off of mirrors, and where the reflected rays either intersect or appear to originate from, will be the location

### Exam 4. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

Name: Class: Date: Exam 4 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Mirages are a result of which physical phenomena a. interference c. reflection

### General Physics Experiment 5 Optical Instruments: Simple Magnifier, Microscope, and Newtonian Telescope

General Physics Experiment 5 Optical Instruments: Simple Magnifier, Microscope, and Newtonian Telescope Objective: < To observe the magnifying properties of the simple magnifier, the microscope and the

### Activity 6.1 Image Formation from Spherical Mirrors

PHY385H1F Introductory Optics Practicals Day 6 Telescopes and Microscopes October 31, 2011 Group Number (number on Intro Optics Kit):. Facilitator Name:. Record-Keeper Name: Time-keeper:. Computer/Wiki-master:..

### Reflectors vs. Refractors

1 Telescope Types - Telescopes collect and concentrate light (which can then be magnified, dispersed as a spectrum, etc). - In the end it is the collecting area that counts. - There are two primary telescope

### Refraction of Light. Refraction of Light

1 Refraction of Light Activity: Disappearing coin Place an empty cup on the table and drop a penny in it. Look down into the cup so that you can see the coin. Move back away from the cup slowly until the

### Exam 4--PHYS 102--S15

Name: Class: Date: Exam 4--PHYS 102--S15 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A mirror produces an upright image. The object is 2 cm high; the

### 1) An electromagnetic wave is a result of electric and magnetic fields acting together. T 1)

Exam 3 Review Name TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. 1) An electromagnetic wave is a result of electric and magnetic fields acting together. T 1) 2) Electromagnetic

### Microscope anatomy, image formation and resolution

Microscope anatomy, image formation and resolution Ian Dobbie Buy this book for your lab: D.B. Murphy, "Fundamentals of light microscopy and electronic imaging", ISBN 0-471-25391-X Visit these websites:

### Mirrors and Lenses. Images can be formed by reflection from mirrors. Images can be formed by refraction through lenses.

Mirrors and Lenses Images can be formed by reflection from mirrors. Images can be formed by refraction through lenses. Notation for Mirrors and Lenses The object distance is the distance from the object

### Optics B. Science Olympiad North Regional Tournament at the University of Florida DO NOT WRITE ON THIS BOOKLET. THIS IS AN TEST SET.

Optics B Science Olympiad North Regional Tournament at the University of Florida 1 DO NOT WRITE ON THIS BOOKLET. THIS IS AN TEST SET. Part I: General Body Knowledge Questions 2 1) (3 PTS) For much of the

### Physics 1230 Homework 8 Due Friday June 24, 2016

At this point, you know lots about mirrors and lenses and can predict how they interact with light from objects to form images for observers. In the next part of the course, we consider applications of

### Basics of Light Microscopy and Metallography

ENGR45: Introduction to Materials Spring 2012 Laboratory 8 Basics of Light Microscopy and Metallography In this exercise you will: gain familiarity with the proper use of a research-grade light microscope

### INDEX OF REFRACTION index of refraction n = c/v material index of refraction n

INDEX OF REFRACTION The index of refraction (n) of a material is the ratio of the speed of light in vacuuo (c) to the speed of light in the material (v). n = c/v Indices of refraction for any materials

### Chapter 34 The Wave Nature of Light; Interference. Copyright 2009 Pearson Education, Inc.

Chapter 34 The Wave Nature of Light; Interference 34-7 Luminous Intensity The intensity of light as perceived depends not only on the actual intensity but also on the sensitivity of the eye at different

### Chapter 36: diffraction

Chapter 36: diffraction Fresnel and Fraunhofer diffraction Diffraction from a single slit Intensity in the single slit pattern Multiple slits The Diffraction grating X-ray diffraction Circular apertures

### NORTHERN ILLINOIS UNIVERSITY PHYSICS DEPARTMENT. Physics 211 E&M and Quantum Physics Spring Lab #8: Thin Lenses

NORTHERN ILLINOIS UNIVERSITY PHYSICS DEPARTMENT Physics 211 E&M and Quantum Physics Spring 2018 Lab #8: Thin Lenses Lab Writeup Due: Mon/Wed/Thu/Fri, April 2/4/5/6, 2018 Background In the previous lab

### CS 443: Imaging and Multimedia Cameras and Lenses

CS 443: Imaging and Multimedia Cameras and Lenses Spring 2008 Ahmed Elgammal Dept of Computer Science Rutgers University Outlines Cameras and lenses! 1 They are formed by the projection of 3D objects.

### Reflection and Refraction of Light

Reflection and Refraction of Light Physics 102 28 March 2002 Lecture 6 28 Mar 2002 Physics 102 Lecture 6 1 Light waves and light rays Last time we showed: Time varying B fields E fields B fields to create

### Instructional Resources/Materials: Light vocabulary cards printed (class set) Enough for each student (See card sort below)

Grade Level/Course: Grade 7 Life Science Lesson/Unit Plan Name: Light Card Sort Rationale/Lesson Abstract: Light vocabulary building, students identify and share vocabulary meaning. Timeframe: 10 to 20

### CHAPTER TWO METALLOGRAPHY & MICROSCOPY

CHAPTER TWO METALLOGRAPHY & MICROSCOPY 1. INTRODUCTION: Materials characterisation has two main aspects: Accurately measuring the physical, mechanical and chemical properties of materials Accurately measuring

### Lecture 3: Geometrical Optics 1. Spherical Waves. From Waves to Rays. Lenses. Chromatic Aberrations. Mirrors. Outline

Lecture 3: Geometrical Optics 1 Outline 1 Spherical Waves 2 From Waves to Rays 3 Lenses 4 Chromatic Aberrations 5 Mirrors Christoph U. Keller, Leiden Observatory, keller@strw.leidenuniv.nl Lecture 3: Geometrical

### OPTICS DIVISION B. School/#: Names:

OPTICS DIVISION B School/#: Names: Directions: Fill in your response for each question in the space provided. All questions are worth two points. Multiple Choice (2 points each question) 1. Which of the

### 13. Optical Instruments*

13. Optical Instruments* Objective: Here what you have been learning about thin lenses is applied to make a telescope. In the process you encounter general optical instrument design concepts. The learning

### a) (6) How much time in milliseconds does the signal require to travel from the satellite to the dish antenna?

General Physics II Exam 3 - Chs. 22 25 - EM Waves & Optics April, 203 Name Rec. Instr. Rec. Time For full credit, make your work clear. Show formulas used, essential steps, and results with correct units

### Assignment X Light. Reflection and refraction of light. (a) Angle of incidence (b) Angle of reflection (c) principle axis

Assignment X Light Reflection of Light: Reflection and refraction of light. 1. What is light and define the duality of light? 2. Write five characteristics of light. 3. Explain the following terms (a)

### Final Reg Optics Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Final Reg Optics Review 1) How far are you from your image when you stand 0.75 m in front of a vertical plane mirror? 1) 2) A object is 12 cm in front of a concave mirror, and the image is 3.0 cm in front

### Phys 531 Lecture 9 30 September 2004 Ray Optics II. + 1 s i. = 1 f

Phys 531 Lecture 9 30 September 2004 Ray Optics II Last time, developed idea of ray optics approximation to wave theory Introduced paraxial approximation: rays with θ 1 Will continue to use Started disussing

### Topic 4: Lenses and Vision. Lens a curved transparent material through which light passes (transmit) Ex) glass, plastic

Topic 4: Lenses and Vision Lens a curved transparent material through which light passes (transmit) Ex) glass, plastic Double Concave Lenses Are thinner and flatter in the middle than around the edges.

### Geometric!Op9cs! Reflec9on! Refrac9on!`!Snell s!law! Mirrors!and!Lenses! Other!topics! Thin!Lens!Equa9on! Magnifica9on! Lensmaker s!formula!

Geometric!Op9cs! Reflec9on! Refrac9on!`!Snell s!law! Mirrors!and!Lenses! Thin!Lens!Equa9on! Magnifica9on! Lensmaker s!formula! Other!topics! Telescopes! Apertures! Reflec9on! Angle!of!incidence!equals!angle!of!reflec9on!

### Lenses- Worksheet. (Use a ray box to answer questions 3 to 7)

Lenses- Worksheet 1. Look at the lenses in front of you and try to distinguish the different types of lenses? Describe each type and record its characteristics. 2. Using the lenses in front of you, look

### Lecture 4: Geometrical Optics 2. Optical Systems. Images and Pupils. Rays. Wavefronts. Aberrations. Outline

Lecture 4: Geometrical Optics 2 Outline 1 Optical Systems 2 Images and Pupils 3 Rays 4 Wavefronts 5 Aberrations Christoph U. Keller, Leiden University, keller@strw.leidenuniv.nl Lecture 4: Geometrical

### =, where f is focal length of a lens (positive for convex. Equations: Lens equation

Physics 1230 Light and Color : Exam #1 Your full name: Last First & middle General information: This exam will be worth 100 points. There are 10 multiple choice questions worth 5 points each (part 1 of

### Rutgers Analytical Physics 750:228, Spring 2013 ( RUPHYS228S13 ) My Courses Course Settings University Physics with Modern Physics, 13e Young/Freedman

Signed in as RONALD GILMAN, Instructor Help Sign Out Rutgers Analytical Physics 750:228, Spring 2013 ( RUPHYS228S13 ) My Courses Course Settings University Physics with Modern Physics, 13e Young/Freedman

### EE-527: MicroFabrication

EE-57: MicroFabrication Exposure and Imaging Photons white light Hg arc lamp filtered Hg arc lamp excimer laser x-rays from synchrotron Electrons Ions Exposure Sources focused electron beam direct write

### CHAPTER 3 OPTICAL INSTRUMENTS

1 CHAPTER 3 OPTICAL INSTRUMENTS 3.1 Introduction The title of this chapter is to some extent false advertising, because the instruments described are the instruments of first-year optics courses, not optical

### PHYS 160 Astronomy. When analyzing light s behavior in a mirror or lens, it is helpful to use a technique called ray tracing.

Optics Introduction In this lab, we will be exploring several properties of light including diffraction, reflection, geometric optics, and interference. There are two sections to this lab and they may

### IMAGE SENSOR SOLUTIONS. KAC-96-1/5" Lens Kit. KODAK KAC-96-1/5" Lens Kit. for use with the KODAK CMOS Image Sensors. November 2004 Revision 2

KODAK for use with the KODAK CMOS Image Sensors November 2004 Revision 2 1.1 Introduction Choosing the right lens is a critical aspect of designing an imaging system. Typically the trade off between image

### Image Formation Fundamentals

03/04/2017 Image Formation Fundamentals Optical Engineering Prof. Elias N. Glytsis School of Electrical & Computer Engineering National Technical University of Athens Imaging Conjugate Points Imaging Limitations

### Education in Microscopy and Digital Imaging

Contact Us Carl Zeiss Education in Microscopy and Digital Imaging ZEISS Home Products Solutions Support Online Shop ZEISS International ZEISS Campus Home Interactive Tutorials Basic Microscopy Spectral

### Image Formation by Lenses

Image Formation by Lenses Bởi: OpenStaxCollege Lenses are found in a huge array of optical instruments, ranging from a simple magnifying glass to the eye to a camera s zoom lens. In this section, we will

QUESTION BANK SCIENCE STD-X PHYSICS REFLECTION & REFRACTION OF LIGHT (REVISION QUESTIONS) VERY SHORT ANSWER TYPE (1 MARK) 1. Out of red and blue lights, for which is the refractive index of glass greater?

### Introduction. Geometrical Optics. Milton Katz State University of New York. VfeWorld Scientific New Jersey London Sine Singapore Hong Kong

Introduction to Geometrical Optics Milton Katz State University of New York VfeWorld Scientific «New Jersey London Sine Singapore Hong Kong TABLE OF CONTENTS PREFACE ACKNOWLEDGMENTS xiii xiv CHAPTER 1:

### Test Review # 9. Physics R: Form TR9.15A. Primary colors of light

Physics R: Form TR9.15A TEST 9 REVIEW Name Date Period Test Review # 9 Light and Color. Color comes from light, an electromagnetic wave that travels in straight lines in all directions from a light source

### O5: Lenses and the refractor telescope

O5. 1 O5: Lenses and the refractor telescope Introduction In this experiment, you will study converging lenses and the lens equation. You will make several measurements of the focal length of lenses and

### Practice Problems for Chapter 25-26

Practice Problems for Chapter 25-26 1. What are coherent waves? 2. Describe diffraction grating 3. What are interference fringes? 4. What does monochromatic light mean? 5. What does the Rayleigh Criterion

### Section 1: Sound. Sound and Light Section 1

Sound and Light Section 1 Section 1: Sound Preview Key Ideas Bellringer Properties of Sound Sound Intensity and Decibel Level Musical Instruments Hearing and the Ear The Ear Ultrasound and Sonar Sound

### Phys214 Fall 2004 Midterm Form A

1. A clear sheet of polaroid is placed on top of a similar sheet so that their polarizing axes make an angle of 30 with each other. The ratio of the intensity of emerging light to incident unpolarized

### Refraction and Lenses

Refraction and Lenses Name Q.(a) Figure shows a ray of light entering a glass block. (i) The angle of incidence in Figure is labelled with the letter i. On Figure, use the letter r to label the angle of

### E X P E R I M E N T 12

E X P E R I M E N T 12 Mirrors and Lenses Produced by the Physics Staff at Collin College Copyright Collin College Physics Department. All Rights Reserved. University Physics II, Exp 12: Mirrors and Lenses

### Section A Conceptual and application type questions. 1 Which is more observable diffraction of light or sound? Justify. (1)

INDIAN SCHOOL MUSCAT Department of Physics Class : XII Physics Worksheet - 6 (2017-2018) Chapter 9 and 10 : Ray Optics and wave Optics Section A Conceptual and application type questions 1 Which is more

### ii) When light falls on objects, it reflects the light and when the reflected light reaches our eyes then we see the objects.

Light i) Light is a form of energy which helps us to see objects. ii) When light falls on objects, it reflects the light and when the reflected light reaches our eyes then we see the objects. iii) Light

### SECTION 1 QUESTIONS NKB.CO.IN

OPTICS SECTION 1 QUESTIONS 1. A diverging beam of light falls on a plane mirror. The image formed by the mirror is a) real, erect b) virtual, inverted c) virtual, erect d) real, inverted. In a pond water