# Chap8_Mirror and Lenses

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1 MIRROR AND LENSES Chapter 8 Contents 8.1 INTRODUCTION 8.2 FLAT MIRROR 8.3 SPHERICAL MIRRORS 8.3.1 SPHERICAL MIRROR EQUATION 8.3.2 SIGN CONVENTION FOR MIRRORS 8.4 THIN LENSES 8.4.1 THIN LENS EQUATION 8.4.2 SIGN CONVENTION FOR LENS 8.5 POWER OF LENSES

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2 Chapter 8 At the end of this chapter you should be able to: Describe the characteristics of plane mirrors Distinguish between converging and diverging spherical mirrors, describe images and their characteristics, and determine these image characteristics using ray diagrams and the spherical mirror equation. Distinguish between converging and diverging lenses, describe images and their characteristics, and find image characteristics using ray diagram and the thin-lens equation Calculate the power of a lens MIRROR AND LENSES

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3 The images of objects formed by optical systems ( mirrors and/or lenses ) can be either real or virtual. real image is one formed by light rays that converge at and pass through the image location, and can be seen or formed on a screen. virtual image is one for which light ray appear to emanate from the image, but do not actually do so. Virtual images cannot be seen or formed on screen. The images of objects can also be upright (erect), inverted, magnified, unmagnified, or reduced in size (diminished) 8.1 INTRODUCTION

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4 All these characteristics can be determined from the lateral magnification For real objects ( these are the only ones with which we will deal ); M < 0 (negative)  the image is real and inverted M > 0 (positive)  the image is virtual and upright |M| > 1  the image is magnified |M| = 1  the image is unmagnified |M| < 1  the image is reduced 8.1 INTRODUCTION

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5 8.2 PLANE MIRROR Mirrors are smooth reflecting surfaces and can reflect beam of light in one direction instead of either scattering it widely into many direction or absorbing it. When one side of a piece of glass is coated with a compound of tin, mercury or silver, its reflectivity is increased and light is not transmitted through the coating. A mirror may be front coated or back coated depending on its applications A plane mirror is a mirror with a flat surface

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6 8.2 PLANE MIRROR A mirror forms an image based on the law of reflection. The characteristics of the images formed by a plane mirror are virtual, upright, and unmagnified, that is M = +1. The image formed by a plane mirror appears to be at a distance behind the mirror that is equal to the distance of the object in front of the mirror and has right-left or front-back reversal. When you look directly into a mirror , what will you see ??

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7 8.2.1 IMAGES FORMED BY PLANE MIRROR The geometry of a mirror’s surface affect the size, orientation, and type of image. Locating a mirror image

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8 What is the minimum length of a plane mirror needed for a person to be able to see his/her complete image ( head to toe) ?

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9 8.3 SPHERICAL MIRRORS A spherical mirror is a section of a sphere. Either the outside ( convex ) surface or the inside ( concave ) surface of the spherical section may be the reflecting surface. concave mirror is called a converging mirror convex mirror is called a diverging mirror

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10 8.3 SPHERICAL MIRRORS principal axis center of curvature ( C ) radius of curvature ( R ) focal length ( f ) The focal point (F)

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11 Principal axis is a line through the center of the spherical mirror that intersects the mirror at the vertex of the spherical section Centre of curvature is the point on the optic axis that corresponds to the center of the sphere of which the mirror forms a section. Radius of curvature is the distance from the vertex to the center of curvature Focal point is the point at which parallel rays converge or appear to diverge.

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12 The images formed by spherical mirrors can be studied from geometry ( ray diagrams ). Three important rays are used to determine the images in a ray diagram: a parallel ray is a ray incident along a path parallel to the optic axis and reflected through the focal point F ( or appear to go through ) a chief ( radial ) ray is a ray incident through the center of curvature C ( or appear to go though ) and reflected back along its incident path through C a focal ray is a ray which passes through ( or appear to go through ) the focal point and is reflected parallel to the optic axis. 8.3 SPHERICAL MIRRORS

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13 8.3 SPHERICAL MIRRORS CONCAVE MIRROR

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14 8.3 SPHERICAL MIRRORS CONVEX MIRROR

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15 8.3 SPHERICAL MIRRORS a) The image is real, inverted, reduced in size, same side as object b) The image is real, inverted, enlarged, same side as object 8.3- (a) IMAGE FORMATION BY A CONCAVE MIRROR

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16 8.3 SPHERICAL MIRRORS c) The image is virtual, upright, enlarged, behind the mirror. What are the characteristics of an image formed, when the object is at F ?

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18 8.3 SPHERICAL MIRRORS a) The image is always virtual, upright, reduced, behind the mirror. 8.3 - (b) IMAGE FORMATION BY A CONVEX MIRROR

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19 8.3 SPHERICAL MIRRORS

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20 8.3 (a) IMAGING CHARACTERISTICS OF CONVEX SPHERICAL MIRRORS Arbitrary upright reduced virtual

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21 8.3 (b) IMAGING CHARACTERISTICS OF CONCAVE SPHERICAL MIRRORS

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22 8.3.1 SPHERICAL MIRROR EQUATION Position and size can be determined by analytical method. do : the object distance (from the object to the vertex) di : the image distance (from the image to the vertex) f : the focal length.

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23 8.3.1 SPHERICAL MIRROR EQUATION

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24 8.3.2 SIGN CONVENTION FOR MIRRORS do is + (do > 0) if the object is in front of the mirror (real object ) do is – (do < 0) if the object is in back of the mirror (virtual object ) di is + (di > 0) if the image is in front of the mirror (real image) di is - (di < 0) if the image is in back of the mirror (virtual image) Both f and R are + if the center of curvature is in front of the mirror (concave mirror) Both f and R are - if the center of curvature is in back of the mirror (convex mirror) If M is +, the image is upright If M is -, the image is inverted

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25 8.3.2 SIGN CONVENTION FOR MIRRORS

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26 True or false? (a) The image of an object placed in front of a concave mirror is always upright. (b) The height of the image of an object placed in front of a concave mirror must be smaller than or equal to the height of the object. (c) The image of an object placed in front of a convex mirror is always upright and smaller than the object. QUICK QUIZ

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27 QUICK QUIZ :ANSWER a) False. A concave mirror forms an inverted image when the object distance is greater than the focal length. b) False. The magnitude of the magnification produced by a concave mirror is greater than 1 if the object distance is less than the radius of curvature. c) True

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28 Example: 1 A 2.0 cm high object is situated 15.0 cm in front of a concave mirror that has radius of curvature of 10.0 cm. Using ray diagram drawn to scale , measure the location and the height of the image Answer: 7.5 cm in front of the mirror Image height : 1.0 cm

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29 Example: 2 Repeat problem 1 for a concave mirror with focal length of 20.0 cm, an object distance of 12.0 cm and a 2.0 cm high object. Answer: 30.0 cm behind the mirror Image height : 5.0 cm , upright

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30 Example: 3 Find the location and describe the characteristic of the image formed by a concave mirror of radius 20.0 cm if the object distance is 30.0 cm 5.0 cm Answer: a) +15 cm , real, M = -1/2 , inverted , reduced in size b) - 10 cm , virtual, M = + 2 , upright , magnified

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31 Example: 4 A concave mirror has a focal length of 20.0 cm . What is the position ( in cm ) of the resulting image if the image is inverted and four times smaller than the object? Answer: 25 cm

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32 8.4. THIN LENSES Made from some transparent material, ex: glass, plastic, crystal, etc. Biconvex lens ( Converging ) Biconcave lens ( Diverging ) Prism base to base Prism point to point

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33 A lens forms an image based on the law of refraction ( Snell's law ). spherical biconvex lens is a converging lens spherical biconcave lens is a diverging lens 8.4. THIN LENSES

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34 8.4. THIN LENSES

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35 Image is real: when formed on the side of the lens opposite the object Image is virtual: when formed of the same side of the lens as the object Three important rays are used to determine the images: a parallel ray is a ray incident along a path parallel to the optic axis and refracted through the focal point F ( or appears to go through ) a chief ( radial ) ray is a ray incident through the center of the lens ( or appears to go through ) and refracted undeviated a focal ray is a ray which passes through ( or appears to go through ) the focal point and is refracted parallel to the principal/optic axis. The intersection of any two of the rays at a point locates the image 8.4. THIN LENSES

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36 8.4. THIN LENSES

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37 CONVERGING LENS 8.4. THIN LENSES

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38 . 8.4. THIN LENSES DIVERGING LENS

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39 8.4. THIN LENSES IMAGE FORMATION BY A CONVEX LENS The image is real The image is inverted

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40 8.4. THIN LENSES IMAGE FORMATION BY A CONVEX LENS The image is virtual The image is upright

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41 8.4 THIN LENSES IMAGE FORMATION BY A CONCAVE LENS The image is virtual The image is upright

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42 8.4.1 THIN LENS EQUATION The thin lens equation is identical in form to the spherical mirror equation

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43 8.4.1 THIN LENS EQUATION The lateral magnification is also defined the same way as for spherical mirrors.

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44 . 8.4.2 SIGN CONVENTION FOR THIN LENS do +ve: real object do -ve: virtual object di +ve: real image di -ve: virtual object Both f and R are +ve : convex lens ( concave mirror ) Both f and R are -ve : concave lens ( convex mirror ) M is +ve: image is upright and on the same side as object M is -ve: image is inverted and on the side of the lens opposite to the object

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45 . 8.4.2 SIGN CONVENTION FOR THIN LENS

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46 . Problem Solving Strategy Be very careful about sign conventions Do lots of problems for practice Draw confirming ray diagrams

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47 . 8.5 POWER OF LENSES Power of lens , Unit: Diopters

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48 Example: 5 An object , O, 4.0 cm high is 20 cm in front of a thin convex lens of focal length +12 cm . Determine the position and height of its image By construction By computation Answer: di=+30 cm, hi=6.0 cm

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49 Example: 6 An object , 9.0 cm high is 27 cm in front of a concave lens of focal length -18 cm . Determine the position and height of its image by the construction and computation. Answer: di= - 10.8 cm, hi= 3.6 cm

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50 Example: 7 A converging lens ( f=20 cm ) is placed 37 cm in front of a screen. Where should the object be placed if its image is to appear on the screen? Answer: 43.5 cm from the lens.

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51 Example: 8 Compute the position and focal length of the converging lens which will project the image of a lamp, magnified 4 times, upon a screen 10.0 cm from the lamp. Answer: do= 2cm, di=8cm f = +1.6cm

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52 . END OF CHAPTER 8