Chapter 23Chapter 23

Mirrors and LensesMirrors and Lenses

Types of Images for Types of Images for Mirrors and LensesMirrors and Lenses

A A real imagereal image is one in which is one in which light light actually passes throughactually passes through the image point the image point Real images can be displayed on screensReal images can be displayed on screens

A A virtualvirtual imageimage is one in which the is one in which the light light does not pass throughdoes not pass through the image point the image point The light appears to come (diverge) from The light appears to come (diverge) from

that pointthat point Virtual images cannot be displayed on Virtual images cannot be displayed on

screensscreens

More About ImagesMore About Images

To find where an To find where an image is formed, it image is formed, it is always is always necessary to necessary to follow at least two follow at least two rays of light as rays of light as they reflect from they reflect from the mirror. the mirror. The The image formed by image formed by the flat mirror is a the flat mirror is a virtual imagevirtual image

Object distance Image distance

Flat MirrorFlat Mirror Simplest possible mirrorSimplest possible mirror Properties of the image Properties of the image

can be determined by can be determined by geometrygeometry

One ray starts at One ray starts at PP, , follows path follows path PQPQ and and reflects back on itselfreflects back on itself

A second ray follows A second ray follows path path PRPR and reflects and reflects according to the Law of according to the Law of ReflectionReflection

p=q!

Properties of the Image Properties of the Image Formed by a Flat MirrorFormed by a Flat Mirror The image is as far behind the mirror The image is as far behind the mirror

as the object is in frontas the object is in front pp = = qq

The image is unmagnified, The image is unmagnified, MM=1=1 The image is virtualThe image is virtual The image is uprightThe image is upright

It has the same orientation as the objectIt has the same orientation as the object There is an apparent left-right reversal There is an apparent left-right reversal

in the imagein the image

Application – Day and Application – Day and Night Settings on Car Night Settings on Car MirrorsMirrors

With the daytime setting, the bright beam of With the daytime setting, the bright beam of reflected light is directed into the driver’s eyesreflected light is directed into the driver’s eyes

With the nighttime setting, the dim beam (With the nighttime setting, the dim beam (DD) ) of reflected light is directed into the driver’s of reflected light is directed into the driver’s eyes, while the bright beam goes elsewhereeyes, while the bright beam goes elsewhere

23.2 Spherical Mirrors23.2 Spherical Mirrors

A A spherical mirrorspherical mirror has the shape of a has the shape of a segment of a spheresegment of a sphere

A A concave concave spherical mirrorspherical mirror has the has the silvered surface of the mirror on the silvered surface of the mirror on the inner, or concave, side of the curveinner, or concave, side of the curve

A A convexconvex spherical mirror spherical mirror has the has the silvered surface of the mirror on the silvered surface of the mirror on the outer, or convex, side of the curveouter, or convex, side of the curve

Concave Mirror, NotationConcave Mirror, Notation

The mirror has a The mirror has a radius radius of curvatureof curvature of of RR

Its Its center of curvaturecenter of curvature is the point is the point CC

Point Point VV is the center of is the center of the spherical segmentthe spherical segment

A line drawn from A line drawn from CC to to VV is called the is called the principle principle axisaxis of the mirror of the mirror

II is the image point is the image point

Focal LengthFocal Length If an object is very far If an object is very far

away, then away, then pp and 1/ and 1/pp 0; 0;

qq==RR/2/2 Incoming rays are Incoming rays are

essentially parallelessentially parallel In this special case, the In this special case, the

image point is called the image point is called the focal pointfocal point

The distance from the The distance from the mirror to the focal point is mirror to the focal point is called the called the focal lengthfocal length The focal length is ½ the The focal length is ½ the

radius of curvature radius of curvature f = R/2

Focal Length Shown by Focal Length Shown by Parallel RaysParallel Rays

23.3 Convex Mirrors23.3 Convex Mirrors A A convexconvex mirror is sometimes called a mirror is sometimes called a

divergingdiverging mirrormirror The rays from any point on the object The rays from any point on the object

diverge after reflection as though they were diverge after reflection as though they were coming from some point behind the mirror coming from some point behind the mirror

The image is virtual because it lies behind The image is virtual because it lies behind the mirrorthe mirror at the point where the reflected at the point where the reflected rays appear to originaterays appear to originate

In general, the image formed by a convex In general, the image formed by a convex mirror is mirror is upright, virtual, and smaller than upright, virtual, and smaller than the objectthe object

Image Formed by a Image Formed by a Convex MirrorConvex Mirror

Ray DiagramsRay Diagrams

A A ray diagramray diagram can be used to can be used to determine the position and size of an determine the position and size of an imageimage

They are graphical constructions which They are graphical constructions which tell the overall nature of the imagetell the overall nature of the image

They can also be used to check the They can also be used to check the parameters calculated from the mirror parameters calculated from the mirror and magnification equationsand magnification equations

Drawing A Ray DiagramDrawing A Ray Diagram

To make the ray diagram, you need to knowTo make the ray diagram, you need to know The position of the objectThe position of the object The position of the center of curvatureThe position of the center of curvature

Three rays are drawnThree rays are drawn They all start from the same position on the They all start from the same position on the

objectobject The intersection of any two of the rays at a The intersection of any two of the rays at a

point locates the imagepoint locates the image The third ray serves as a check of the The third ray serves as a check of the

constructionconstruction

The Rays in a Ray The Rays in a Ray DiagramDiagram

Ray 1 is drawn parallel Ray 1 is drawn parallel to the principle axis to the principle axis and is reflected back and is reflected back through the focal through the focal point, point, FF

Ray 2 is drawn through Ray 2 is drawn through the focal point and is the focal point and is reflected parallel to the reflected parallel to the principle axisprinciple axis

Ray 3 is drawn through Ray 3 is drawn through the center of curvature the center of curvature and is reflected back and is reflected back on itselfon itself

1

3

2

Notes About the RaysNotes About the Rays

The rays actually go in all The rays actually go in all directions from the objectdirections from the object

The three rays were chosen for The three rays were chosen for their ease of constructiontheir ease of construction

The image point obtained by the The image point obtained by the ray diagram must agree with the ray diagram must agree with the value of value of qq calculated from the calculated from the mirror equationmirror equation

Ray Diagram for Concave Ray Diagram for Concave Mirror, Mirror, pp > > RR

The image is realThe image is real The image is invertedThe image is inverted The image is smaller than the objectThe image is smaller than the object

Ray Diagram for a Ray Diagram for a Concave Mirror, Concave Mirror, pp < < ff

The image is virtualThe image is virtual The image is uprightThe image is upright The image is larger than the objectThe image is larger than the object

Ray Diagram for a Convex Ray Diagram for a Convex MirrorMirror

The image is virtualThe image is virtual The image is uprightThe image is upright The image is smaller than the objectThe image is smaller than the object

Notes on ImagesNotes on Images With a concave mirror, the image may be either With a concave mirror, the image may be either

real or virtualreal or virtual When the object is outside the focal point, the image When the object is outside the focal point, the image

is realis real When the object is at the focal point, the image is When the object is at the focal point, the image is

infinitely far away (to the left in the previous infinitely far away (to the left in the previous diagrams)diagrams)

When the object is between the mirror and the focal When the object is between the mirror and the focal point, the image is virtualpoint, the image is virtual

With a convex mirror, the image is always With a convex mirror, the image is always virtual and uprightvirtual and upright As the object distance increases, the virtual image As the object distance increases, the virtual image

gets smallergets smaller