Mirrors And LensesMirrors And Lenses

Chapter 23Chapter 23

IntroductionIntroduction

Images can be formed by plane or Images can be formed by plane or spherical mirrors and by lenses.spherical mirrors and by lenses.– Ray diagrams will be usedRay diagrams will be used

Plane and Curved MirrorsPlane and Curved Mirrors

Important terms:Important terms:– Object distance Object distance (p)(p)

– ImageImage» Formed where light rays actually intersect or Formed where light rays actually intersect or

where they appear to originatewhere they appear to originate

– Image distance Image distance (q)(q)

Two Types of ImagesTwo Types of Images

Real imageReal image– Light rays actually intersect and pass Light rays actually intersect and pass

through the image point.through the image point.

– May be formed on a screenMay be formed on a screen

Virtual ImageVirtual Image– Light rays only appear to come from the Light rays only appear to come from the

image point.image point.

– Cannot be formed on a screenCannot be formed on a screen

»Example: Example: images in flat mirrorsimages in flat mirrors

Flat MirrorsFlat Mirrors

The image distanceThe image distance (q)(q) always equals always equals the object distancethe object distance (p).(p).

23.1, 29.123.1, 29.1

The image heightThe image height (h’)(h’) always always equals the object heightequals the object height (h).(h).

23.223.2

Images are left-right reversed.Images are left-right reversed.

Images are always virtual.Images are always virtual.

186186

Images are always upright.Images are always upright.

MagnificationMagnification (M) (M) is always 1.is always 1.

h

hM

′=

Flat Mirrors SummaryFlat Mirrors Summary

The image distance always equals the object The image distance always equals the object distance.distance.

The image height The image height (h’)(h’) always equals the object always equals the object height height (h).(h).

Images are left-right reversed.Images are left-right reversed. Images are always virtual.Images are always virtual. Images are always upright.Images are always upright. Lateral magnification Lateral magnification (M)(M) is always 1. is always 1.

h

hM

′=

Applications of Flat MirrorsApplications of Flat Mirrors

Rearview mirrors in carsRearview mirrors in carsDressing room mirrorsDressing room mirrorsBathroom mirrorsBathroom mirrors

242, 29.2242, 29.2

Concave MirrorsConcave Mirrors

Concave mirrors are a part of a Concave mirrors are a part of a sphere.sphere.

236, 380236, 380

Light reflects from the inner Light reflects from the inner surface.surface.

Images formed may be real or Images formed may be real or virtual.virtual.– The type of image depends upon the The type of image depends upon the

object location.object location.

Images may be upright or inverted.Images may be upright or inverted.

Concave mirrors are sometimes Concave mirrors are sometimes called converging mirrors.called converging mirrors.

The focal length is positive.The focal length is positive.

Concave Mirrors SummaryConcave Mirrors Summary

Are a part of a sphere Are a part of a sphere Light reflects from the inner surface.Light reflects from the inner surface. Images formed may be real or virtual.Images formed may be real or virtual.

– Depends upon object locationDepends upon object location Images may be upright or inverted.Images may be upright or inverted. Sometimes called converging mirrorsSometimes called converging mirrors Focal length is positive.Focal length is positive.

Important TermsImportant Terms

Principal axisPrincipal axis Image pointImage point Image distance Image distance (q)(q) Object distance Object distance (p)(p) Center of curvature Center of curvature CC Radius of curvature Radius of curvature RR Focal point Focal point (F)(F) Focal length Focal length (f)(f)

23.923.9 2

Rf =

Spherical AberrationSpherical Aberration

Spherical aberration is an undesirable Spherical aberration is an undesirable characteristic that is present in all characteristic that is present in all spherical mirrorsspherical mirrors

» It may be eliminated by using It may be eliminated by using parabolicparabolic mirrors.mirrors.

Parabolic Mirror ApplicationsParabolic Mirror Applications

Satellite dishesSatellite dishes Car headlightsCar headlights FlashlightsFlashlights Projector bulbsProjector bulbs Astronomical telescopesAstronomical telescopes

Ray DiagramsRay Diagrams

Front side and back side of the mirrorFront side and back side of the mirror– Light rays are always in Light rays are always in frontfront of the of the

mirror.mirror.» This is taken to be the left side.This is taken to be the left side.

Three Important RaysThree Important Rays

The intersection of any two rays will The intersection of any two rays will locate the image.locate the image.

Parallel rays that come from infinity Parallel rays that come from infinity always pass through the focal pointalways pass through the focal point– When the object is at infinity, the image When the object is at infinity, the image

is at the focal pointis at the focal point

382, 188, 382, 383382, 188, 382, 383

The paths of light rays are The paths of light rays are reversible.reversible.

238238

Equations for Concave Equations for Concave MirrorsMirrors

Magnification equation:Magnification equation:

The mirror equationThe mirror equation

€

M =′ h

h= −

q

p

f

1

q

1

p

1=+

Applications of Concave Applications of Concave MirrorsMirrors

Shaving mirrorsShaving mirrors Makeup mirrorsMakeup mirrors Solar cookersSolar cookers

Convex MirrorsConvex Mirrors

Convex mirrors are a part of a Convex mirrors are a part of a sphere.sphere.

380380

Light reflects from the outer Light reflects from the outer surface.surface.

Images formed are always virtual.Images formed are always virtual.– They always lie behind the mirror.They always lie behind the mirror.

Images are always upright.Images are always upright.

Convex mirrors are sometimes Convex mirrors are sometimes called diverging mirrors.called diverging mirrors.

The focal length is negative.The focal length is negative.

Convex Mirrors SummaryConvex Mirrors Summary

Are a part of a sphereAre a part of a sphere Light reflects from the outer surfaceLight reflects from the outer surface Images formed are always virtualImages formed are always virtual

– They always lie behind the mirror.They always lie behind the mirror. Images are always uprightImages are always upright Sometimes called diverging mirrorsSometimes called diverging mirrors Focal length is negativeFocal length is negative

Ray Diagrams for Convex Ray Diagrams for Convex MirrorsMirrors

Front side and back side of the mirrorFront side and back side of the mirror– Light rays are always in front of the Light rays are always in front of the

mirror.mirror.

Ray DiagramsRay Diagrams

See Figure 23.11See Figure 23.11– Three important rays Three important rays (see pg. 765)(see pg. 765)

23.11, 240, 384, 23.1223.11, 240, 384, 23.12

Rays that come from infinity Rays that come from infinity always pass through the focal always pass through the focal point.point.– When the object is at infinity, the When the object is at infinity, the

image is at the focal point.image is at the focal point.

The intersection of two rays will The intersection of two rays will locate the image.locate the image.

Equations for Convex MirrorsEquations for Convex Mirrors

These equations are the same as before.These equations are the same as before.– Magnification equationMagnification equation

– The mirror equationThe mirror equation

p

q

h

hM −=

′=

f

1

q

1

p

1=+

Sign Conventions for MirrorsSign Conventions for Mirrors

SeeSee Table 23.1Table 23.1 on page 765on page 765

Applications of Applications of Convex Convex MirrorsMirrors

Side view mirrors on carsSide view mirrors on carsShoplifting mirrorsShoplifting mirrors

QuestionsQuestions

1 - 4, 71 - 4, 7

Pg. 783Pg. 783

Images Formed By RefractionImages Formed By Refraction

Sign conventionsSign conventions– See See Table 23.2 Table 23.2 on page 770on page 770

Apparent DepthApparent Depth

Flat refracting surfacesFlat refracting surfaces – Apparent DepthApparent Depth (q)(q) vs. Actual Depthvs. Actual Depth (p)(p)

» nn11 is below the surface is below the surface

23.16, 24323.16, 243

€

q = −pn2

n1

⎛

⎝ ⎜

⎞

⎠ ⎟

Atmospheric RefractionAtmospheric Refraction

The Sun is not where it appears to be.The Sun is not where it appears to be.– It can be seen even though it is below the It can be seen even though it is below the

horizon.horizon. Sun dogs and Moon dogsSun dogs and Moon dogs

– Halos on cold winter days or nightsHalos on cold winter days or nights» Refraction through hexagonal ice crystalsRefraction through hexagonal ice crystals

MiragesMirages

23.2123.21

Thin LensesThin Lenses

A A thin lensthin lens is a piece of glass or plastic is a piece of glass or plastic which is ground so that its surfaces are which is ground so that its surfaces are segments of either spheres or planes.segments of either spheres or planes.– A thin lens acts like two prisms.A thin lens acts like two prisms.

Refraction in Optical InstrumentsRefraction in Optical Instruments

Thin lenses are used to form images by Thin lenses are used to form images by refractionrefraction in optical instrumentsin optical instruments– CamerasCameras– ProjectorsProjectors– MicroscopesMicroscopes– TelescopesTelescopes– BinocularsBinoculars– Magnifying glassesMagnifying glasses

248, 249248, 249

The Thin Lens EquationThe Thin Lens Equation

The lens equation is The lens equation is virtually identicalvirtually identical to the mirror equation.to the mirror equation.

23.2323.23

f

1

q

1

p

1=+

Common Lens ShapesCommon Lens Shapes Converging lensesConverging lenses

– BiconvexBiconvex– Convex-concaveConvex-concave– Plano-convexPlano-convex

Diverging lensesDiverging lenses– BiconcaveBiconcave– Convex-concaveConvex-concave– Plano-concavePlano-concave

»

64, 66, 6764, 66, 67

Convex LensesConvex Lenses

Convex lensesConvex lenses form virtual images when the form virtual images when the object is within the focal length of the lens.object is within the focal length of the lens.– Example: a simple magnifying glass.Example: a simple magnifying glass.

Convex lensesConvex lenses form real images when the form real images when the object is beyond the focal length of the lens.object is beyond the focal length of the lens.

250250

Concave LensesConcave Lenses

Concave lensesConcave lenses never form real images. never form real images.

251251

Thin Lens ConceptsThin Lens Concepts

Focal pointFocal point (F)(F)– Thin lenses have two.Thin lenses have two.

– Parallel light rays pass through the lens Parallel light rays pass through the lens and converge or appear to originate here.and converge or appear to originate here.

Focal lengthFocal length (f)(f)

6868

Magnification EquationMagnification Equation

Equation for magnification:Equation for magnification:

p

q

h

hM −=

′=

Thin Lens EquationThin Lens Equation

Thin-lens equation:Thin-lens equation:

f

1

q

1

p

1=+

Lens Maker’s EquationLens Maker’s Equation

RR11 is for the is for the surfacesurface closest to the object closest to the object

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛−−=

21 R

1

R

11n

f

1

The The frontfront of the lens of the lens– The side from which light approachesThe side from which light approaches

Sign ConventionsSign Conventions

Sign conventions Sign conventions (Table 23.3) pg. 775(Table 23.3) pg. 775– ExtremelyExtremely important! important!

Ray DiagramsRay Diagrams

Ray diagrams Ray diagrams (similar to mirrors)(similar to mirrors)– Three important raysThree important rays– Rays that come from infinity always pass Rays that come from infinity always pass

through the focal point.through the focal point.» When the object is at infinity, the image is at or When the object is at infinity, the image is at or

appears to be at the focal point.appears to be at the focal point.

– The intersection of two rays will locate the The intersection of two rays will locate the image.image.

247, 23.25, 69, 70 247, 23.25, 69, 70

Thin Lens CombinationsThin Lens Combinations

The image formed by the first The image formed by the first lens serves as thelens serves as the “object”“object” for for the second lens.the second lens.

256256

AA location diagramlocation diagram is definitely is definitely useful when determining puseful when determining p22..

252252

Total Magnification of Thin Lens Total Magnification of Thin Lens CombinationsCombinations

Formula:Formula:

21mmMT =

Spherical AberrationSpherical Aberration Similar to that produced by mirrorsSimilar to that produced by mirrors

– In mirrors, it can be reduced by using In mirrors, it can be reduced by using parabolic surfaces.parabolic surfaces.» Parabolic mirrors are used in headlights, Parabolic mirrors are used in headlights,

satellite dishes, searchlights, and satellite dishes, searchlights, and astronomical mirrors.astronomical mirrors.

» Parabolic surfaces are more expensive to Parabolic surfaces are more expensive to make.make.

23.3023.30

In lenses, spherical aberration may In lenses, spherical aberration may be reduced by using a small be reduced by using a small aperture size.aperture size.

Chromatic AberrationChromatic Aberration

Chromatic aberration results because Chromatic aberration results because different wavelengths have different indices different wavelengths have different indices of refraction.of refraction.

Chromatic aberration is produced by lenses Chromatic aberration is produced by lenses but not by mirrors.but not by mirrors.

Chromatic Aberration may be reduced by Chromatic Aberration may be reduced by using combinations of converging and using combinations of converging and diverging lenses made from different types diverging lenses made from different types of glassof glass– This is expensive.This is expensive.

QuestionsQuestions

9 - 13 9 - 13

Pg. 784Pg. 784