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Chapter 3: Mirrors

Please remember to photocopy 4 pages onto one sheet by going A3A4 and using back to back on the photocopier

Draw a diagram of a book sitting on a table with a stick person beside it, and a light-bulb higher up.

Show, using arrowed lines on the diagram, how the person sees the book.

Lets imagine its a blue book and a light-bulb which emits white light. Why does the book appear blue?

Questions to make you think

. Why does shoe polish !a yucky mucky substance" make your shoes shiny?

#. When both you and your friend look at the same blue book, is there any way to show that both you and your

friend see the same colour?

$. Did you know that you can look back in time % in fact youre doing so right now.

&ou could e'en build an instrument to allow you to see yourself as you were #( years ago)

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Student Notes

Reflectionis defined as the bouncing of light off an ob*ect

When light hits off most e'eryday ob*ects it scatters in all directions % this is known as diffuse reflection, but when

the surface it shines off is flat and sil'ered % a plane mirror % then it beha'es in a much more predictable way.

+n fact, we can say two things for definite about it these two things are known as he Laws of /eflection of Light.

Laws of Reflection of Light*

. he incident ray, the normal at the point of incidenceand the reflected ray all lie on the same plane.

#. he angle of incidence is e0ual to the angle of

reflection !1 ".

he image formed !y a plane mirror is called a "#irtual image$ *

2or a plane mirror, the image is as far behind the mirror as the ob*ect is in front3

%ow an image is formed in a &lane Mirror*

45am 6uestion7 What can you see in a plane mirror?

Student answer7 /ows of seats and the wings

#

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Spherical Mirrors

here are two types of spherical mirror Concaveand Convex.

8 conca'e mirror ca'es in at the centre !as you look at it", whereas a con'e5 mirror bulges out.

Real and 'irtual (mages*

) Real (mage is an image formed !y the actual intersection of light rays

8 real image can be located on a screen.

) #irtual image is formed !y the apparentintersection of light rays

8 'irtual image cannot be formed on a screen !because there are no actual rays to intersect behind the mirror"

Conca#e Mirrors + ray diagrams

+n order to find out what an image of an ob*ect will look like after reflection from a spherical mirror, we draw two

following simple rules, and where these lines intersect represents the position of the image.

&ou should be able to draw a ray diagram showing how a conca'e mirror forms an image of an ob*ect which is placed

!i" outside the focus % resulting in a real image

!ii" inside the focus % resulting in a 'irtual image

wo Rules*

!i" 2rom top of ob*ect to mirror !parallel to principal a5is" back through the focus.

!ii" 2rom top of ob*ect, hitting the mirror on the principle a5is and back out at same angle on the other side.

2or each of the following label the centre of curvature!9", thefocus !f", the Objectand theImage.

:ote that the focus is half-way between the centre of curvatureand the vertex!the 'erte5 is the point where the

principle a5is meets the mirror".

Note

;ust put a 'ery slight cur'ature on the mirror to begin with, or better still make the mirror a straight line while

drawing the rays, and only afterwards put in a slight cur'e.

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,!-ect insidethe focus + #irtual image

:otice that when the ob*ect is inside the focal point the light rays ne'er intersect, but from the 'iewers perspecti'e

they appear to do sobehind the mirror!the 'iewer is to the left of the mirror in the diagrams abo'e".

Note

8 real image is always in front of the mirror and in'erted.

8 'irtual image is always behind the mirror and upright.

.ses of Conca#e Mirrors

/ Searchlights

0 1loodlights

3 %eadlights in a car

2 Sha#ing and makeup mirrors4 dentist$s mirror.

2or applications % $ abo'e the light bulb is placed at the focus this means that all light going backwards from the

bulb hits the mirror and gets reflected back out parallel to the principal a5is instead of spreading out in all directions.

tooth inside the focus the image is magnified and upright.

=

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Con#e5 Mirrors + ray diagrams

ere only one diagram is needed the image is always diminished, upright and 'irtual.

wo Rules

!i" 2rom top of ob*ect to mirror parallel to principle a5is back up as if coming from the focus on the other side.

!ii" 2rom top of ob*ect, hitting the mirror on the principle a5is and back out at same angle on the other side.

:otice that in this situation !similar to the conca'e mirror when the ob*ect is inside the focus" the light rays ne'er

intersect, but from the 'iewers perspecti'e they appear to do so!ehind the mirror.

he image is therefore always #irtual, regardless of where the ob*ect is placed.

.ses of Con#e5 Mirrors

/ 6oor mirror of a car0 (n shops to deter shoplifters

3 )t concealed entrances to gi#e a #iew of oncoming traffic

8ll of these are based on the principle that a con'e5 mirror gi'es a wide field of 'iew, e'en if does gi'e a diminished

image.

Maths &ro!lems

Relationship !etween focal length 7f84 o!-ect distance 7u8 and image distance 7#8 for spherical mirrors

vuf

+=

"Real is Positivecon#ention 7R(&8 for the image distance #

When using the formula abo'e, if you are told the image distance and know that the image is real, make the number

positi'e, but if you know that the image is 'irtual then make the number negati'e.

@

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+f on the other hand ' is what you are looking for, then whether it turns out positi'e or negati'e will determine

whether it is a real or 'irtual image.

Mandatory 95periment: o Aeasure the focal length of a 9onca'e Airror

B

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M9)S.R9M9N ,1 %9 1,C)L L9N% ,1 ) C,NC)'9 M(RR,R

)&&)R).S: 9onca'e mirror, screen, lamp-bo5 with crosswire, metre stick, retort stand.

6()R)M

&rocedure

1irst find an appro5imate #alue for the focal length

2ocus the image of a distant ob*ect onto a screen. Aeasure the distance between the mirror and the screen.

his corresponds to an appro5imate 'alue for the focal length of the mirror.

.

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Lea#ing Cert &hysics Sylla!us

Content 6epth of reatment )cti#ities SS

. Laws of /eflection Demonstration using ray

bo5 or laser or other

suitable method.

#. Airrors +mages formed by plane

and spherical mirrors.

vuf +=

u

vM =

/eal-is-positi'e sign

con'ention.

Simple e5ercises onmirrors by ray tracing or

use of formula.

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95tra Credit

6id you know that you can look !ack in timeuestions: Mirrors

. M#((@ NLO

!i" What is meant by the reflection of light?

!ii" State the laws of reflection of light.

!iii" Describe an e5periment to demonstrate one of the laws of reflection of light.

#. M#((@O

8n ob*ect N is placed $( cm in front of a conca'e mirror of focal length ( cm. ow far from the mirror is the

image formed?

$. M#((= NLO

8 conca'e mirror has a focal length of #( cm. 8n ob*ect is placed $( cm in front of the mirror. ow far from the

mirror will the image be formed?

=. M#((= NLO

se a ray diagram to show the formation of a real image by a conca'e mirror.

@. M#((B NLO

9opy and complete in your answer-book the following diagram to show how a conca'e mirror

forms an image of an ob*ect N, which is placed outside the focus 2 of the mirror.

B. M#(($ NLO M#((F NLO

Describe the image that is formed in a conca'e mirror when an ob*ect is placed inside the focus.

F. M#((IO Draw a ray diagram to show the formation of an image in a con'e5 mirror.

G. M#((= NLO

8 conca'e mirror can produce a real or a 'irtual image, depending on the position of the ob*ect.

Ei'e one difference between a real image and a 'irtual image.

I. M#((= NLO Ei'e two uses for a conca'e mirror.

(. M#((# NLOM#(( NLO8 student carried out an e5periment to measure the focal length of a conca'e mirror.

he student placed an ob*ect at different positions in front of the mirror so that a real image was formed in each

case.

he table shows the measurements recorded by the student for the ob*ect distance u and the image distance '.

u>cm #

(

$

(

=

(

@

(

'>cm B

=

=

$

=

$

@

!i" Draw a labelled diagram showing how the apparatus was arranged.

!ii" Describe how the student found the position of the image.

!iii" Show on your diagram the ob*ect distance u and the image distance '.

!i'" sing the formula or otherwise and the abo'e data, find an a'erage 'alue for the focal length f of

the mirror.

. M#((FO

+n an e5periment to measure the focal length of a conca'e mirror, an appro5imate 'alue for the focal length was

found. he image distance ' was then found for a range of 'alues of the ob*ect distance u.

he following data was recorded.

!i" ow was an appro5imate 'alue for the focal lengthfound?

!ii" What was the ad'antage of finding the appro5imate 'alue for the focal length?

#

u>c

m

@.( #(.( #@.( $(.( $@.( =(.(

'>cm

B(.@ $(.( #$.( #(.@ G.( B.@

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!iii" Describe, with the aid of a labelled diagram, how the position of the image was found.

!i'" 9alculate the focal length of the conca'e mirror graph based on the recorded data.

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95am solutions: Mirrors

.

!i" /eflection is the bouncing of light from a surface.

!ii" he incident ray, the normal at the point of incidence and the reflected ray all lie on the same plane.

he angle of incidence is e0ual to the angle of reflection !i 1 r".

!iii" 8pparatus7 raybo5, mirror.

f >$( P >' 1 >( ' 1 @ cm 1 (.@ m

$. vuf

+=

>#( 1 >$( P >' ' 1 B( cm

=.

@.

? he image is 'irtual, magnified and upright.

F.

G. 8 real image can be obtained on a screen a 'irtual image cannot.

+n a real image the light rays meet in a 'irtual image they do not.

8 real image is always in'erted> a 'irtual is erect, a real image is in front > a 'irtual image is behind.

@ orch, headlights, searchlight, dentist mirror, cosmetic mirror, solar furnace.

(.

!i" See diagram!ii" he position of the screen was ad*usted until the image of the cross-wires

came into focus.

!iii"See diagram.

!i'" >f7 (.(BB, (.(@F, (.(=I, (.(=I f7 @.#, F.BF, #(.#, #(.B

a'erage 'alue for f 1 G.= cm.

.

!i" 8n image of a distant ob*ect was focused on a screen.

Aeasure the distance from the screen to the mirror.

!ii" o a'oid placing ob*ect inside f during the e5periment" which would

ha'e meant that the image couldnt be formed on the screen.

!iii" 8pparatus7 ob*ect, conca'e mirror, screen8d*ust the position of the the screen until a clear image of the crosswire

is obtained.

!i'"

2ocal length 1 #.( cm

=

u>cm @.( #(.( #@.

(

$(.( $@.( =(.(

'>cm B(.@ $(.( #$.

(

#(.@ G.( B.@

>u

>'

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