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ContentsINTRODUCTION

FLAT MIRRORSPHERICAL MIRRORSSPHERICAL MIRROR EQUATIONSIGN CONVENTION FOR

MIRRORS THIN LENSES THIN LENS EQUATION SIGN CONVENTION FOR LENS POWER OF LENSES

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At the end of this chapter you should be able to:

Describe the characteristics of plane mirrors Describe the characteristics of plane mirrors

Distinguish between converging and diverging spherical Distinguish between converging and diverging spherical mirrors,mirrors, describe images and their characteristics, and determine describe images and their characteristics, and determine these these image characteristics using ray diagrams and the image characteristics using ray diagrams and the spherical mirror spherical mirror equation.equation.

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Describe the nature of image formed Describe the nature of image formed by plane mirrors.by plane mirrors.

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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

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Mirrors are smooth reflecting surfaces and Mirrors are smooth reflecting surfaces and can reflect beam of light in one direction can reflect beam of light in one direction instead of either scattering it widely into instead of either scattering it widely into many direction or absorbing it.many direction or absorbing it.

When one side of a piece of glass is coated with a When one side of a piece of glass is coated with a compound of tin, mercury or silver, its reflectivity iscompound of tin, mercury or silver, its reflectivity isincreased and light is not transmitted through increased and light is not transmitted through the coating.the coating.

A mirror may be front coated or back coated A mirror may be front coated or back coated depending on its applicationsdepending on its applications

A plane mirror is a mirror with a flat surface

• As light ray strikes the surface of the plane mirror, what happens to the ray?

• How plane mirror is produced?

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•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 hasright-left or front-back reversal.

When you look directly into a mirror , When you look directly into a mirror , what will you see ?what will you see ?

LEFT- RIGHT REVERSAL

Draw a ray Draw a ray diagram as diagram as basis.basis.

• Characterize the images formed in a plane mirror.

• What is left-right reversal or front-back reversal?

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The geometry of a mirror’s surface affect the size,The geometry of a mirror’s surface affect the size,orientation, and type of image.orientation, and type of image.

Locating a mirror imageLocating a mirror image

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

• Kaleidoscopic effect, with multiple images formed.

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Multiple Reflections Multiple Reflections ( 2 or more mirrors)( 2 or more mirrors)

objectobject

imageimage

imageimage

imageimage

Web Link: Multiple reflectionsWeb Link: Multiple reflections

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

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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.

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• Give examples of converging mirror and diverging mirror.

• Describe a concave and convex mirror.

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principal axis center of curvature ( C )

radius of curvature ( R )

focal length ( f )

The focal point (F)

Focal pointFocal point

FF

vertexvertex

ff

RR

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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,

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Rf

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______________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,

2

Rf

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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.

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a) The image is real, inverted, reduced in size, a) The image is real, inverted, reduced in size, same side as objectsame side as object

b) The image is real, inverted, enlarged, b) The image is real, inverted, enlarged, same side as objectsame side as object

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c) The image is virtual, upright, enlarged, c) The image is virtual, upright, enlarged, behind the mirror.behind the mirror.

What are the characteristics of an image formed, What are the characteristics of an image formed, when the object is at F ?when the object is at F ?

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a) The image is always virtual, upright, reduced, a) The image is always virtual, upright, reduced, behind the mirror.behind the mirror.

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Convex Mirror

Object location Image orientation Image size Image type

IMAGING CHARACTERISTICS OF CONVEX IMAGING CHARACTERISTICS OF CONVEX SPHERICAL MIRRORSSPHERICAL MIRRORS

ArbitraryArbitrary uprightupright reduced reduced virtualvirtual

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Concave Mirror

Object location Image orientation Image size Image type

Beyond C Inverted Reduced Real

At C Inverted Same as object Real

Between F and C Inverted Enlarged Real

Just beyond F Inverted Approaching infinity

Real

Just inside F Upright Approaching infinity

Virtual

Between mirror and F

Upright Enlarged Virtual

8.3 (b) IMAGING CHARACTERISTICS OF 8.3 (b) IMAGING CHARACTERISTICS OF CONCAVE SPHERICAL MIRRORSCONCAVE SPHERICAL MIRRORS

• 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

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Spherical MirrorsSpherical Mirrors

(Mirror Formulae)(Mirror Formulae)

concave concave sideside

convex convex sideside

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

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: Construct ray diagrams to locate and describe the

image formed by the spherical mirrors.

Group 5

Group 6

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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?

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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?

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Rfdd io

2111

Position and size can be determined by Position and size can be determined by analytical method.analytical method.

fd

fddor

o

oi

do : the object distance (from the object to the vertex)

di : the image distance (from the image to the vertex)

f : the focal length.

40o

oo

o

o

o

i

o

i

df

fm

fd

fd

fd

fdm

d

d

h

hm

)(/)(

To determine the magnification and orientation of the To determine the magnification and orientation of the objectobject

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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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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.

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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

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?

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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

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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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Example: 1Example: 1

A 2.0 cm high object is situated 15.0 cm A 2.0 cm high object is situated 15.0 cm in front of a concave mirror that has radius in front of a concave mirror that has radius of curvature of 10.0 cm. Using ray diagram of curvature of 10.0 cm. Using ray diagram drawn to scale , measuredrawn to scale , measure

a)a) the location andthe location andb)b) the height of the imagethe height of the image

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Example: 2Example: 2

Repeat problem 1 for a concave mirror with Repeat problem 1 for a concave mirror with focal length of 20.0 cm, an object distance of focal length of 20.0 cm, an object distance of 12.0 cm and a 2.0 cm high object.12.0 cm and a 2.0 cm high object.

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Example: 3Example: 3

Find the location and describe the characteristic Find the location and describe the characteristic of the image formed by a concave mirror of radiusof the image formed by a concave mirror of radius20.0 cm if the object distance is 20.0 cm if the object distance is

a)a) 30.0 cm30.0 cmb)b) 5.0 cm5.0 cm

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Example: 4Example: 4

A concave mirror has A concave mirror has a focal length of 20.0 a focal length of 20.0 cm .cm .

What is the position What is the position ( in cm ) of the ( in cm ) of the resulting image if the resulting image if the image is inverted and image is inverted and four times smaller four times smaller than the object?than the object?

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Made from some transparent material, ex: glass, plastic, crystal, etc.

1R 2R1R

2R

Biconvex lensBiconvex lens( Converging )( Converging )

Biconcave lensBiconcave lens( Diverging )( Diverging )

Prism base to basePrism base to base Prism point to pointPrism point to point

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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

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Image is realImage is real: when formed on the side of the lens opposite the object: when formed on the side of the lens opposite the object

Image is virtualImage is virtual: when formed of the same side of the lens as the object: 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 The intersection of any two of the rays at a point

locates the imagelocates the image

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.

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• The image is real• The image is inverted

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• The image is virtual• The image is upright

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• The image is virtual• The image is upright

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• The thin lens equation is identical in form to the spherical mirror equation

fd

fdd

fdd

o

oi

io

111

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• The lateral magnification is also defined the same way as for spherical mirrors.

o

i

o

i

d

d

h

h

heightobject

heightimageM

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.

do +ve: real objectdo +ve: real object

do -ve: virtual objectdo -ve: virtual object

di +ve: real imagedi +ve: real image

di -ve: virtual objectdi -ve: virtual object

Both f and R are +ve : convex lens ( concave mirror )Both f and R are +ve : convex lens ( concave mirror )

Both f and R are -ve : concave lens ( convex mirror )Both f and R are -ve : concave lens ( convex mirror )

M is +ve: image is upright and on the same side as objectM is +ve: image is upright and on the same side as object

M is -ve: image is inverted and on the side of the M is -ve: image is inverted and on the side of the lens lens opposite to the objectopposite to the object

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.

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

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.

Problem Solving Strategy

• Be very careful about sign conventions– Do lots of problems for practice

• Draw confirming ray diagrams

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.

)(

1

meterfp

Power of lens , Power of lens ,

Unit: Unit: DioptersDiopters

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Example: 5Example: 5

An object , O, 4.0 cm high is 20 cm in front of a thin An object , O, 4.0 cm high is 20 cm in front of a thin convex lens of focal length +12 cm . Determine the convex lens of focal length +12 cm . Determine the position and height of its imageposition and height of its imagea)a) By constructionBy constructionb)b) By computationBy computation

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Example: 6Example: 6

An object , 9.0 cm high is 27 cm in An object , 9.0 cm high is 27 cm in front of a concave lens of focal length -front of a concave lens of focal length -18 cm . Determine the position and 18 cm . Determine the position and height of its image by the construction height of its image by the construction and computation.and computation.

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Example: 7Example: 7

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

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Example: 8Example: 8

Compute the position and focal length Compute the position and focal length of the converging lens which will of the converging lens which will project the image of a lamp, magnified project the image of a lamp, magnified 4 times, upon a screen 10.0 cm from 4 times, upon a screen 10.0 cm from the lamp.the lamp.

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.

END OF CHAPTER 8END OF CHAPTER 8