Physics 132: Lecture Fundamentals of Physics IIameyerth/phy132s16/Lect18.pdf · Physics 132: Lecture Fundamentals of Physics II Agenda for Today Mirrors Concave Con eConvex Mirror

Physics 132: Lecture Fundamentals of Physics

IIIIAgenda for Today

MirrorsMirrorsConcave

Con eConvexMirror equation

Physics 201: Lecture 1, Pg 1

Curved mirrorsA Spherical Mirror: section of a sphere.

R principal

light ray Concave mirror

p paxis•

C

light ray Convex i

principal axis

mirror

C•


C = Center of curvatureIn front of concave mirror, behind convex mirror.

Concave Mirror Raysy1) Parallel to principal axis reflects through f.2) Through f, reflects parallel to principal axis.

O

) g , p p p

3) Through center.

#1O

fc

#1

#2#3

I

cImage is:

Real (light rays actually cross)ea ( g t ays actua y c oss)Inverted (Arrow points opposite directionDiminished (smaller than object)


**Any other ray from object tip which hits mirror will reflect through image tip

Mirror Equation

do = distance object is from mirror (+ in front - behind)di = distance image is from mirror (+ in front - behind)

f = focal length of mirror (+ in front - behind)

OMirror Equation:

do

di distance image is from mirror (+ in front behind)

O1

do

1di

1f f

c

I

o i c

An arrow is placed 6 cm in front of a concave mirror with focal length f=2 cm Determine the image location diwith focal length f 2 cm. Determine the image location.

111 d 3 i f t f i


cm 2cm 6

iddi = 3 cm in front of mirror

Clicker Question 1:A concave mirror brings the sun's rays to a focus in front of the

mirror. Suppose the mirror is submerged in a swimming pool but still pointed up at the sun.p p

Will the sun's rays be focused nearer to, farther from, or at the same distance from the mirror?

(a) Nearer to the mirror(a) Nearer to the mirror (b) The same distance from the mirror(c) Farther from the mirror.


Signs(Mirrors) Object ObjectPositive: in front of mirrorNegative: behind mirror (oops! using a concave asNegative: behind mirror (oops! using a concave as

a convex or vice versa) Focal length Focal lengthPositive: Concave mirrorNegative: Convex MirrorNegative: Convex Mirror

ImagePositive: in front of mirrorPositive: in front of mirrorNegative: behind mirror


Generally, call the object’s side of the mirror the + direction, and then all the other signs follow

PCQ: Clicker Question 2When you look at your reflection in the bowl of a spoon, it is

upside down. (1) Why?

(2) Where is your head relative to the focal length of the spoon?

a. closer to the spoon than the focal lengthb f th f th th th f l l thb. further away from the spoon than the focal lengthc. at the focal length


Magnification= hi/hoD hi h t ik i t P A

do

Draw ray which strikes mirror at P.A.

OhoAngle of incidence

di

do

Ihi

Angle of reflectionh h di

o

o

dh

)tan(i

i

dh

dh


m positive if uprightm negative if inverted

26o

i

o

i

dd

hh m

Clicker Question 3:A negative magnification for a mirror means that

A. the image is inverted, and the mirror is concave.B. the image is inverted, and the mirror is convex.C. the image is inverted, and the mirror may be

concave or convex.D. the image is upright, and the mirror may be

concave or convex.th i i i ht d th i iE. the image is upright, and the mirror is convex.


Clicker 4:Where in front of a concave mirror should you place an object

so that the image is virtual?

A. Object close to mirror

B. Object far from mirror

C. Either close or far

D. Never


Convex Mirror Rays y1) Parallel to principal axis reflects through f.2) Through f, reflects parallel to principal axis.) g , p p p

3) Through center.#1

OI#2 #3

cImage is:Virtual (light rays don’t really cross)

fVirtual (light rays don t really cross)Upright (same direction as object)Diminished (smaller than object)


**For a real object, image is always virtual, upright and diminished

Mirror Equationd di t bj t i f i ( i f t b hi d)d0 = distance object is from mirror (+ in front - behind)

di = distance image is from mirror (+ in front - behind)f f l l th f i ( i f t b hi d)

d0

f = focal length of mirror (+ in front - behind)

OMirror Equation: OI1

do

1di

1f

An arrow is placed 6 cm in front of a convex mirror with focal length f=-3 cm Determine the image location

fo i

difocal length f 3 cm. Determine the image location.

di = -2 cm 111


i

Behind mirrorcm 3cm 6

id

Clicker 5:Where should you place an object in front of a convex

mirror to produce a real image?

1) Object close to mirror

2) Object far from mirror

3) Either close or far)

4) You can’t


Clicker Question 6:You see an upright, magnified image of your face when you look into magnifying “cosmetic mirror.”

The image is located

A. In front of the mirror’s surface.B. On the mirror’s surface.

C. Behind the mirror’s surface.D. Only in your mind because it’s a virtual image.


Clicker Question 7:The rear-view mirrors on the passenger side of many cars have

a warning statement: "OBJECTS IN MIRROR ARE CLOSER THAN THEY APPEAR." This means that the nature of the mirror must be

A. concave.B. plane.C. convex.D. transparent.


Mirror Summary

A l f i id A l f R fl ti Angle of incidence = Angle of Reflection Principal RaysParallel to P.A.: Through focus Through focus: Parallel to P.A. Through center: Back on self

|f| = R/2 1/f = 1/do + 1/di

Behind mirror is negative, in front is positive


m = -di / do

39

Example:An object's image in a 24 cm -focal-length concave mirror is

upright and magnified by a factor of 3.0. How far is the object from the mirror?


Converging Lens

All rays parallel to principal axis pass through focal point F

n1 n1

>P.A.

F

n2>n1

F

Physics 201: Lecture 1, Pg 18Double Convex

Converging Lens Principal Rays

F I

F

F

Object

ImageP.A.

1) Rays parallel to principal axis pass through focal point1) Rays parallel to principal axis pass through focal point.2) Rays through center of lens are not refracted.3) Rays through F emerge parallel to principal axis.3) Rays through F emerge parallel to principal axis.

Assumptions:

Image is real, inverted and enlarged


Assumptions:

• monochromatic light incident on a thin lens.

• rays are all “near” the principal axis.

Ray tracing for a converging lens

Thi ld b d iThis could be used in a camera

This could be used as a projector

This is a magnifying glass


Cli k Q iClicker Question 7:

A concave mirror has a positive focal length f>0A convex mirror has a negative focal length f<0What is the focal length of a flat mirror?What is the focal length of a flat mirror?

A) f =0 B) f =


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Physics 132: Lecture Fundamentals of Physics IIameyerth/phy132s16/Lect18.pdf · Physics 132: Lecture Fundamentals of Physics II Agenda for Today Mirrors Concave Con eConvex Mirror