Chapter 34A Chapter 34A -- Reflection Reflection and Mirrors (Geometrical)and Mirrors (Geometrical)

A PowerPoint Presentation by

Paul E. Tippens, Professor of Physics

Southern Polytechnic State University

A PowerPoint Presentation byA PowerPoint Presentation by

Paul E. Tippens, Professor of PhysicsPaul E. Tippens, Professor of Physics

Southern Polytechnic State UniversitySouthern Polytechnic State University

© 2007

Objectives: Objectives: After completing this After completing this module, you should be able to:module, you should be able to:

•• Explain and discuss with diagrams, Explain and discuss with diagrams, reflectionreflection, , absorptionabsorption, and , and refractionrefraction of light rays.of light rays.

•• Define and illustrate your understanding of Define and illustrate your understanding of realreal, , virtualvirtual, , erecterect, , invertedinverted, , enlargedenlarged, and , and diminisheddiminished as applied to images.as applied to images.

•• Use geometrical optics to draw images of an Use geometrical optics to draw images of an object at various distances from object at various distances from convergingconverging and and divergingdiverging mirrors.mirrors.

•• Illustrate graphically the reflection of light Illustrate graphically the reflection of light from from planeplane, , convexconvex, and , and concaveconcave mirrors.mirrors.

Geometrical OpticsGeometrical Optics

In the study of how light behaves, it is useful to use “light rays” and the fact that light travels in straight lines.

In the study of how light behaves, it is In the study of how light behaves, it is useful to use useful to use ““light rayslight rays”” and the fact and the fact that light travels in straight lines.that light travels in straight lines.

When light strikes the When light strikes the boundary between boundary between two media, three two media, three things may happen: things may happen: reflectionreflection, , refractionrefraction, , or or absorptionabsorption..

reflection

refraction

absorption Water

Air

Reflection, Refraction, and Reflection, Refraction, and AbsorptionAbsorption

Water

AirReflection:Reflection: A ray A ray from air strikes from air strikes the water and the water and returns to the air.returns to the air.

Refraction:Refraction: A ray A ray bends into the bends into the water toward the water toward the normal line.normal line.

Absorption:Absorption: A ray is A ray is absorbed atomically absorbed atomically by the water and by the water and does not reappear.does not reappear.

reflection

refraction

absorption Water

Air reflection

refraction

absorption

The Laws of ReflectionThe Laws of Reflection

Water

Air1. The angle of 1. The angle of inciinci-- dencedence ii is equal is equal to the angle of to the angle of reflection reflection rr ::

i = r i = r

i

N reflection

r

All ray angles are measured with respect to normal All ray angles are measured with respect to normal NN..

2. The incident ray, the 2. The incident ray, the reflected ray, and reflected ray, and the normal the normal NN all lie all lie in the same plane.in the same plane.

3. The rays are 3. The rays are completely completely reversible.reversible.

The Plane MirrorThe Plane MirrorA A mirrormirror is a highly polished surface that is a highly polished surface that forms images by uniformly reflected light.forms images by uniformly reflected light.

Note: images appear to be equi-distant behind mirror and are right- left reversed.

DefinitionsDefinitionsObject distance:Object distance: The straightThe straight--line distance line distance pp from the surface of a mirror to the object. from the surface of a mirror to the object.

Image distance:Image distance: The straightThe straight--line distance line distance qq from the surface of a mirror to the image. from the surface of a mirror to the image.

Object distance

Image distance=

p = q

i = r

ObjectObject ImageImage

pp qq

Real and VirtualReal and VirtualReal imagesReal images and and objects are formed objects are formed by actual rays of by actual rays of light. (Real images light. (Real images can be projected on can be projected on a screen.)a screen.)

Virtual imagesVirtual images and and objects do not really objects do not really exist, but only seem exist, but only seem to be at a location.to be at a location.

Virtual images are on the Virtual images are on the oppositeopposite side of the mirror side of the mirror from the incoming rays.from the incoming rays.

Real object

Virtual image

Light rays No light

Image of a Point ObjectImage of a Point Object

Plane mirror

Real object

p

Image appears to be at same distance behind mirror regardless of viewing angle. Image appears to be at same distance Image appears to be at same distance behind mirror regardless of viewing angle.behind mirror regardless of viewing angle.

q Virtual image

q = p

Image of an Extended ObjectImage of an Extended Object

Plane mirror

p q

Image of bottom and top of guitar shows forward-back, right-left reversals. Image of bottom and top of guitar Image of bottom and top of guitar shows forwardshows forward--back, rightback, right--left reversals.left reversals.

q = p

Virtual image

Terms for Spherical MirrorsTerms for Spherical MirrorsA A spherical mirrorspherical mirror is is formed by the inside formed by the inside ((concaveconcave) or outside ) or outside ((convexconvex) surfaces of ) surfaces of a sphere.a sphere.

A A concave spherical concave spherical mirrormirror is shown here is shown here with parts identified.with parts identified.

Concave Mirror

Radius of curvature RVertex V

Center of Curvature CThe The axisaxis and and linear linear apertureaperture are shown.are shown.

Linear aperture

V

C

R Axis

The Focal Length The Focal Length ff of a Mirrorof a Mirror

axis

r

iR

Incident parallel ray

f

The focal length, f

The focal The focal length length f f is:is:

2Rf

The focal length f is equal to half the radius RThe focal length f is equal to half the radius R

Since Since ii = = rr , we , we find that find that FF is midis mid-- way between way between VV and and CC; we find:; we find:C VF

Focal point

For objects lo- cated at infinity, the real image appears at the focal point since rays of light are almost parallel.

For objects loFor objects lo-- catedcated at at infinityinfinity, , the the realreal image image appears at the appears at the focal pointfocal point since since rays of light are rays of light are almost parallel.almost parallel.

The Focus of a Concave MirrorThe Focus of a Concave MirrorThe focal point The focal point FF for a concave mirror is the point for a concave mirror is the point at which all parallel light rays at which all parallel light rays convergeconverge..

axis

Incident parallel Rays

CF

Focal pointFocal point 2Rf

The Focus of a Convex MirrorThe Focus of a Convex MirrorThe The focal pointfocal point for a convex mirror is the point for a convex mirror is the point F F from which all parallel light rays from which all parallel light rays divergediverge..

axisC F

RR

Incident Rays

Reflected Rays

Virtual focus; reflected rays diverge.

2Rf

Image Construction:Image Construction:

Ray 1: A ray parallel to mirror axis passes through the focal point of a concave mirror or appears to come from the focal point of a convex mirror.

Ray 1:Ray 1: A ray parallel to mirror axis passes A ray parallel to mirror axis passes through the focal point of a concave mirror through the focal point of a concave mirror or appears to come from the focal point of a or appears to come from the focal point of a convex mirror.convex mirror.

C F

Convex mirror

Object

C F

Concave mirror

Object

Ray 1Ray 1

Image Construction (Cont.):Image Construction (Cont.):

Ray 2: A ray passing through the focus of a concave mirror or proceeding toward the focus of a convex mirror is reflected parallel to the mirror axis.

Ray 2:Ray 2: A ray passing through the focus of a A ray passing through the focus of a concave mirror or proceeding toward the concave mirror or proceeding toward the focus of a convex mirror is reflected parallel focus of a convex mirror is reflected parallel to the mirror axis. to the mirror axis.

Concave mirror

C FRay 2

Ray 1

Image C F

Convex mirror

Ray 2

Ray 1

Image

Image Construction (Cont.):Image Construction (Cont.):

Ray 3: A ray that proceeds along a radius is always reflected back along its original path. Ray 3:Ray 3: A ray that proceeds along a radius is A ray that proceeds along a radius is always reflected back along its original path. always reflected back along its original path.

C F

Convex mirror

Concave mirror

C F

Ray 2

Ray 1

Ray 3

Ray 3

C FRay 2

Ray 1

Image

The Nature of ImagesThe Nature of ImagesAn object is placed in front of a concave mirror. It is useful to trace the images as the object moves ever closer to the vertex of the mirror.

An object is placed in front of a concave mirror. An object is placed in front of a concave mirror. It is useful to trace the images as the object It is useful to trace the images as the object moves ever closer to the vertex of the mirror.moves ever closer to the vertex of the mirror.

We will want to locate the image and answer three questions for the possible positions:

3. Is it enlarged, diminished, or the same size?

2. Is the image real or virtual?

1. Is the image erect or inverted?

Object Outside Center CObject Outside Center C

Concave mirror

C FRay 3

Ray 2

Ray 11. The image is 1. The image is invertedinverted; ; i.e., opposite of the i.e., opposite of the object orientation.object orientation.

2. The image is 2. The image is realreal; i.e., ; i.e., formed by actual light formed by actual light rays in front of mirror. rays in front of mirror.

3. The image is 3. The image is diminished diminished in size; i.e., smaller in size; i.e., smaller than the object.than the object.

Image is located between C and F Image is located between C and F

Object at the Center CObject at the Center C

C F

Ray 2

Ray 11. The image is 1. The image is invertedinverted; ; i.e., opposite of the i.e., opposite of the object orientation.object orientation.

2. The image is 2. The image is realreal; i.e., ; i.e., formed by actual light formed by actual light rays in front of mirror. rays in front of mirror.

3. The image is 3. The image is the same the same size size as the object.as the object. Image is located

at C, inverted. Image is located at C, inverted.

Ray 3

Object Between C and FObject Between C and F1. The image is 1. The image is invertedinverted; ;

i.e., opposite of the i.e., opposite of the object orientation.object orientation.

2. The image is 2. The image is realreal; i.e., ; i.e., formed by actual light formed by actual light rays in front of mirror. rays in front of mirror.

3. The image is 3. The image is enlarged enlarged in size; i.e., larger than in size; i.e., larger than the object.the object.

Image is outside of the center C Image is outside of the center C

C F

Ray 1Ray 3

Ray 2

Object at Focal PointObject at Focal Point

Image is located at infinity (not formed). Image is located at infinity (not formed).

C

F

Ray 3

Reflected rays are parallel

When the object is located at the focal point of the mirror, the image is not formed (or it is located at infinity).

When the object is When the object is located at the focal located at the focal point of the mirror, point of the mirror, the image is the image is not not formedformed (or it is (or it is located at infinity).located at infinity).

The parallel reflected The parallel reflected rays never cross.rays never cross.

Ray 1

Object Inside Focal PointObject Inside Focal Point1. The image is 1. The image is erecterect; ;

i.e., same orientation i.e., same orientation as the object.as the object.

2. The image is 2. The image is virtualvirtual; ; that is, it seems to be that is, it seems to be located located behindbehind mirror.mirror.

3. The image is 3. The image is enlarged; enlarged; bigger than the object.bigger than the object.

Image is located behind the mirror Image is located behind the mirror

C

FErect and enlarged

Virtual image

Observe the Images as Observe the Images as Object Moves Closer to MirrorObject Moves Closer to Mirror

Concave mirror

C FRay 3

Ray 2

Ray 1

C F

Ray 2

Ray 1

Ray 3

C F

Ray 1Ray 3

Ray 2

C

F

Ray 3

Reflected rays are parallel

Ray 1

C

FErect and enlarged

Virtual image

Convex Mirror ImagingConvex Mirror Imaging

C F

Convex mirror

Ray 2

Ray 1

Image

All images are erect, virtual, and diminished. Images get larger as object approaches.

All images are All images are erecterect, , virtualvirtual, and , and diminisheddiminished. . Images get larger as object approaches.Images get larger as object approaches.

C F

Convex mirror

Ray 1

2

Image gets larger as object gets

closer

Converging and Diverging MirrorsConverging and Diverging MirrorsConcave Concave mirrors and mirrors and converging parallel rays will converging parallel rays will be called be called converging mirrorsconverging mirrors from this point onward.from this point onward.

ConvexConvex mirrors and mirrors and diverging parallel rays will diverging parallel rays will be called be called diverging mirrorsdiverging mirrors from this point onward.from this point onward.

CF

Converging Mirror

Concave

C F

Diverging Mirror

Convex

SummarySummaryReflection:Reflection: A ray A ray from air strikes from air strikes the water and the water and returns to the air.returns to the air.

Refraction:Refraction: A ray A ray bends into the bends into the water toward the water toward the normal line.normal line.

Absorption:Absorption: A ray is A ray is absorbed atomically absorbed atomically by the water and by the water and does not reappear.does not reappear.

Water

Air reflection

refraction

absorption

Summary (Cont.)Summary (Cont.)

Water

Air1. The angle of 1. The angle of inciinci-- dencedence ii is equal is equal to the angle of to the angle of reflection reflection rr ::

i = r i = r

i

N reflection

r

All ray angles are measured with respect to normal All ray angles are measured with respect to normal NN..

2. The incident ray, the 2. The incident ray, the reflected ray, and reflected ray, and the normal the normal NN all lie all lie in the same plane.in the same plane.

3. The rays are 3. The rays are completely completely reversible.reversible.

Summary (Definitions)Summary (Definitions)

Object distance:Object distance: The straightThe straight--line distance line distance pp from the surface of a mirror to the object. from the surface of a mirror to the object.

Image distance:Image distance: The straightThe straight--line distance line distance qq from the surface of a mirror to the image.from the surface of a mirror to the image.

Real image:Real image: An image formed by real light An image formed by real light rays that can be projected on a screen. rays that can be projected on a screen.

Virtual image:Virtual image: An image that appears to be at An image that appears to be at a location where no light rays reach. a location where no light rays reach.

Converging and diverging mirrors:Converging and diverging mirrors: Refer to the Refer to the reflection of parallel rays from surface of mirror.reflection of parallel rays from surface of mirror.

Image Construction Summary:Image Construction Summary:

Ray 1: A ray parallel to mirror axis passes through the focal point of a concave mirror or appears to come from the focal point of a convex mirror.

Ray 1:Ray 1: A ray parallel to mirror axis passes A ray parallel to mirror axis passes through the focal point of a concave mirror through the focal point of a concave mirror or appears to come from the focal point of a or appears to come from the focal point of a convex mirror.convex mirror.

Ray 2: A ray passing through the focus of a concave mirror or proceeding toward the focus of a convex mirror is reflected parallel to mirror axis.

Ray 2:Ray 2: A ray passing through the focus of a A ray passing through the focus of a concave mirror or proceeding toward the concave mirror or proceeding toward the focus of a convex mirror is reflected parallel focus of a convex mirror is reflected parallel to mirror axis. to mirror axis.

Ray 3: A ray that proceeds along a radius is always reflected back along its original path. Ray 3:Ray 3: A ray that proceeds along a radius is A ray that proceeds along a radius is always reflected back along its original path. always reflected back along its original path.

Summary (Cont.)Summary (Cont.)For plane mirrors, the object distance equals For plane mirrors, the object distance equals the image distance and all images are erect and the image distance and all images are erect and virtual.virtual.

For converging mirrors and diverging mirrors, For converging mirrors and diverging mirrors, the focal length is equal to onethe focal length is equal to one--half the radius.half the radius.

All images formed from convex mirrors are All images formed from convex mirrors are erect, virtual, and diminished in size.erect, virtual, and diminished in size.

Except for objects located inside the focus Except for objects located inside the focus (which are erect and virtual), all images formed (which are erect and virtual), all images formed by converging mirrors are real and inverted. by converging mirrors are real and inverted.

CONCLUSION: Chapter 34ACONCLUSION: Chapter 34A Reflection and Mirrors Reflection and Mirrors

(Geometrical)(Geometrical)