MIRROR AND LENSES Contents INTRODUCTION FLAT MIRROR SPHERICAL MIRRORS SPHERICAL MIRROR EQUATION SIGN CONVENTION FOR MIRRORS THIN LENSES THIN LENS EQUATION SIGN CONVENTION FOR LENS POWER OF LENSES

MIRROR AND LENSES 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.

Describe the nature of image formed by plane mirrors.

INTRODUCTION 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)

Contrast real image and virtual image.Give examples. Virtual images: images formed by a plane mirror Real Images: image formed by the LCD projector

PLANE MIRROR A plane mirror is a mirror with a flat surface 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. Flat mirror is a mirror with a flat surface , 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 coated. A mirror maybe front coated or back coated Depending on its applications. When you look directly in to a mirror, you will see the reflected images of yourself And objects around you. A mirror may be front coated or back coated depending on its applications

As light ray strikes the surface of the plane mirror, what happens to the ray? How plane mirror is produced?

PLANE MIRROR When you look directly into a mirror , what will you see ? 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. Flat mirror is a mirror with a flat surface , 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 coated. A mirror maybe front coated or back coated Depending on its applications. When you look directly in to a mirror, you will see the reflected images of yourself And objects around you. 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.

LEFT- RIGHT REVERSAL AMBULANCE Draw a ray diagram as basis.

Characterize the images formed in a plane mirror. What is left-right reversal or front-back reversal?

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

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) ?

Kaleidoscopic effect, with multiple images formed.

Multiple Reflections ( 2 or more mirrors) object image image image Web Link: Multiple reflections

When mirror surfaces are curved instead of flat, strange things happen……

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

Why concave mirror is also called converging mirror? Rays parallel to the principal axis reflect from the concave mirror and meet or converge at the real focus F. Why convex mirror is also called diverging mirror? Rays parallel to principal axis hit a convex mirror, the reflected ray spread out or diverge.

Give examples of converging mirror and diverging mirror. Describe a concave and convex mirror.

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

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. Focal length is the distance from the focal point to the vertex of the spherical section. It is equal to one-half of the radius of curvature,

______________is a line through the center of the spherical mirror that intersects the mirror at the vertex of the spherical section ______________is the point on the optic axis that corresponds to the center of the sphere of which the mirror forms a section. ______________ is the distance from the vertex to the center of curvature ______________ is the point at which parallel rays converge or appear to diverge. ______________ is the distance from the focal point to the vertex of the spherical section. It is equal to one-half of the radius of curvature,

SPHERICAL MIRRORS The images formed by spherical mirrors can be studied from geometry ( ray diagrams/ ray tracing ). 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 CONCAVE MIRROR

8.3 SPHERICAL MIRRORS CONVEX MIRROR

IMAGE FORMATION BY A CONCAVE MIRROR SPHERICAL MIRRORS IMAGE FORMATION BY A CONCAVE MIRROR 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 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 ?

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

8.3 SPHERICAL MIRRORS

IMAGING CHARACTERISTICS OF CONVEX SPHERICAL MIRRORS Convex Mirror Object location Image orientation Image size Image type Arbitrary upright reduced virtual

8.3 (b) IMAGING CHARACTERISTICS OF CONCAVE SPHERICAL MIRRORS Concave Mirror Object location Image orientation Image size Image type Beyond C Inverted Reduced Real At C Same as object Between F and C Enlarged Just beyond F Approaching infinity Just inside F Upright Virtual Between mirror and F

How would you compare the images formed in a side mirror of the car with that of a plane mirror? Plane mirror: virtual, upright, unmagnified. Car’s side mirror: virtual, upright, diminished

Spherical Mirrors (Mirror Formulae) concave side convex side

Group 1 Group 3 Group 2 Group 4 C F C F Review: Construct ray diagrams to locate and describe the image formed by the spherical mirrors. Group 1 Group 3 C F C F Group 2 Group 4 C F C F

: Construct ray diagrams to locate and describe the image formed by the spherical mirrors. Group 5 Group 6 C F C F

Recall: 2. How will you describe the image formed by convex mirror in all location of the object? 3. What are the 3 specific rays drawn used to find location, size, and orientation of the image in a curved mirrors?

Starter: How would you explain an inverted image using the ray diagram? How would you be able to distinguish a virtual image from a real image using the ray diagrams?

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

SPHERICAL MIRROR EQUATION To determine the magnification and orientation of the object

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

SIGN CONVENTION FOR MIRRORS

Sample Problems: 1. Santa checks himself for soot, using his reflection in a shiny silvered Christmas tree ornament 0.0750 m away. The diameter of the ornament is 7.20 cm. Standard reference work state that he is “ right jolly old elf,” so we estimate his height too be 1.6 m. where and how tall is the image of Santa formed by the ornament? Is it erect or inverted? 2. A magnified, inverted image is located a distance of 32.0 cm from a concave mirror with a focal length of 12.0 cm. Determine the object distance and tell whether the image is real or virtual.

QUIZ 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.

Quiz 1. Determine the image distance and image height for a 5.00-cm tall object placed 45.0 cm from a concave mirror having a focal length of 15.0 cm. 2. A concave mirror forms an image on a wall 3.00 m from the mirror of the filament of a head light lamp 10.0 cm in front of the mirror. (a) What are the radius of curvature and focal length of the mirror? (b) What is the height of the image if the height of the object is 5.0 mm?

3. In a laboratory experiment, it is desired to form an image that is one-half as large as an object. How far must the object be held from a diverging mirror of radius 40 cm? 4. What is the magnification of an object if it is located 10 cm from a mirror and its image is erect and seems to be located 40 cm behind the mirror? Is the mirror diverging or

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

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

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.

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

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?

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

8.4. THIN LENSES 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

Three important rays are used to determine the images: 8.4. THIN LENSES 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

8.4. THIN LENSES CONVERGING LENS

8.4. THIN LENSES DIVERGING LENS .

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

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

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

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

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

8.4.2 SIGN CONVENTION FOR THIN LENS di +ve: real image do +ve: real object do -ve: virtual object 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

8.4.2 SIGN CONVENTION FOR THIN LENS Quantity Positive When Negative When Object location (p) Object is in front of the lens Object is in back of the lens Image location (q) Image is in back of the lens ( real image ) Image is in front of the lens ( virtual image ) Image height (h’) Image is upright and on the same side as object Image is inverted and opposite the object R1 and R2 Center of curvature is in back of the lens Center of curvature is in front of the lens Focal length (f) Converging lens Diverging lens .

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

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

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

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.

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?

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. M= l di / d0 l = 4 di=+4do do+di=10 d0+4d0=10 do=10/5=2, di=10-2=8cm

END OF CHAPTER 8 .