03images and curved mirrors

7/28/2019 03images and Curved Mirrors

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DIAGNOSTIC /REMEDIAL TEST

03 IMAGES AND CURVED MIRRORS

This test is one of a series in Introductory Physics made available on the Website of the School

of Physics, Monash University, Australia (www.physics.monash.edu.au/community).This test is NOT for the purposes of assessment. It is to assist you in locating misconceptions

and misunderstandings and generally to assist you in your study of Physics. You should work

by yourself and at your own pace following the directions given. It is not necessary to attempt

the test all at once. You may like to do it bit-by-bit, waiting until you have covered a particular

topic in class or in your reading of your text book or you may like to "plunge in " before you

begin your study of the topic.

Questions are on the left hand (even-numbered) pages. While reading or working on these,

keep the right hand (odd-numbered) answer page covered. DO NOT PEEK AT THE

ANSWERS ON THE RIGHT HAND PAGE !

The test was compiled by and largely authored by Emeritus Professor Bill Rachinger who would

appreciate any comments or suggestions for improvement. These could be sent to him at

[email protected] or

Emeritus Professor Bill Rachinger, School of Physics

Monash University, P.O.Box 27, Vic 3800 Australia

Diagrams were produced by

Mr Steve McCausland, formerly of Department of Physics, Monash University


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COVER THE RIGHT HAND (ODD-NUMBERED) PAGES

DO NOT PEEK

1.

The Figure shows fine beams of light striking an arrangement of small pieces of mirror. The

normals (perpendiculars) to these are shown dotted. Draw in the reflected beams accurately

making use of the laws of reflection.

GO STRAIGHT TO THE NEXT QUESTION. DON'T CHECK YOUR ANSWER YET.

WAIT UNTIL YOU ARE INSTRUCTED TO DO SO.

2.

Consider now broad beams of light striking four of the pieces of mirror. Draw in the reflections

of these beams.

CHECK YOUR ANSWERS TO THE LAST GROUP OF QUESTIONS. REFER TO THE

APPROPRIATE SECTIONS OF YOUR TEXT BOOK FOR FURTHER INFORMATION.

Fig. 1

Fig 2


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1.

This shows how parallel fine beams of light can be made to converge to a point by using an

arrangement of small flat mirrors.

2

This shows how the beams have converged. Note that they have not converged to a point as in

the previous question but have converged to a region in the vicinity of this point.

Fig 3

Fig 4


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Interlude:

The two previous questions give a lead as to how to make a "converging" mirror. If a

mirror is continuously curved rather than composed of small flat pieces it is possible to focus aparallel beam of light to a sharp point.

Refer back to the Figures of the previous questions and think about the effect of replacing the

pieces of flat mirror with a smooth curve. This is shown in Fig.5. This shows the principle of

operation of a converging mirror. Any ray parallel to the axis AB of this mirror will pass

through the point F, known as the principal focus. A small spherical mirror will behave

approximately in this way.

In the lower half of Fig 5 you can see that a light ray originating at F such as the ray FC will,

after reflection, travel parallel to the axis AB. This is an illustration of the reversibility of lightrays i.e. if a light ray is "sent back on its tracks" it will follow the same path.

Fig 5


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It is usual in ray diagrams to represent the curved mirror by a single line (shown dotted in

Figure 6) and to make use of the construction that any ray parallel to the axis AB will be

reflected (at the dotted line) so as to pass through F and any ray passing through F will after

reflection be directed parallel to AB. These are important rules for the construction of ray

diagrams and the location of images.

The representation of the mirror by a straight line is, of course, an approximation but this is, for

many purposes, quite adequate. Nature is often very complex and in order to analyse or

investigate many physical situations you will need to approximate to the true situation by

neglecting certain features.

Fig 6


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3.

The figure shows an arrangement of small plane mirrors struck by fine beams of light coming

from a luminous object O.

Draw in the reflected rays accurately using the laws of reflection.

CHECK YOUR ANSWERS TO THIS QUESTION. REFER TO THE APPROPRIATE

SECTIONS OF YOUR TEXT BOOK FOR FURTHER INFORMATION.

Fig 7


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3.

Light diverging from the object O is reflected and converges and passes through the point I.

Here again you could imagine the effect of replacing the pieces of flat mirror with a curved

mirror. All rays diverging from O would, after reflection, pass through the point I. If you put

your eye at the point P so as to capture some of these you would see a bright spot at I. If a piece

of white paper were placed at I a bright spot would appear on it. You would in either case be

seeing an image of the luminous object O. Such an image is known as a real image. It is an

image through which light actually passes. You may like to think of a real image as one which

can be "captured" on a translucent screen such as a sheet of tissue.

Compare this real image with an image of your face as seen in a flat mirror described earlier.

When light rays appear to come from an image but do not actually pass through it, the image is

known as a virtual image. Such an image can not, of course be "captured" on a screen.

A curved mirror which would focus the object O at I is of a very special shape, based on an

ellipse. The same light rays diverging from O striking a small spherical mirror would behave in

approximately the same way. In the following questions we will deal with converging mirrorswhich we assume to behave ideally like very small spherical mirrors.

Fig 8


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4.

A luminous object is placed at the point O in front of an ideal (small) concave spherical mirror

whose principal focus is at F. Two rays are drawn from O, one parallel to the axis AB and the

other passing through F. These strike the mirror (represented by the dotted line). Draw in the

reflected rays and locate the image of the object O.



5.

Consider now an extended object, an arrow as indicated in the Figure. Draw rays from the two

points on it and decide what form the image takes.



Fig 9

Fig 10


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4.

Ray OD will be reflected through F and ray OF after striking the "mirror" at E will travel

parallel to the axis of the mirror. These will intersect at I, the image of O. Note that the ray OA

shown dotted will after reflection pass through I.

5.

The two points on the arrow are imaged as shown in the Figure so that the image of the arrow is

the inverted arrow shown. It is not necessary in a ray tracing exercise to locate the images of a

series of points on the object. One point, for example the tip of the arrow, is sufficient.

Fig 11

Fig 12


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6.

Locate the position of the image of the object O by drawing a ray diagram and then answer the

following questions.

a) Is the image larger, smaller or the same size as the object? ............

b) Is the image erect or inverted? ............

c) Is the image real or virtual? .............

d) Would the image be visible to an eye looking towards the mirror as represented by L ?...

e) Would the image be visible to an eye M looking away from the mirror?...

f) Would the image be visible to an eye N looking behind the mirror?...

g) Does light pass through the image?.........

h) Could the image be made visible on a screen (or a piece of white paper)?.........



Fig 13


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6.

a) Larger.

b) Inverted.

c) Real, see also answer g).

d) Yes, light rays passing through the image would reach an eye (represented by L)

looking towards the mirror .

e) No, light rays passing through the image would not reach the eye at M.

f) No, light rays passing through the image would not reach the eye at N.

g) Yes.

h) Yes, in the same way as an image is formed on a movie screen.(This image could then be seen by the eye at M)

Fig 14


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7.






d) Would the image be visible to an eye looking towards the mirror represented by L ?...




h) Could the image be made visible on a screen (or a piece of white paper)?..........

GO STRAIGHT TO THE NEXT QUESTION. DON'T CHECK YOUR ANSWERS YET.


Fig 15


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7.

a) Smaller

b) Inverted.


d) Yes, light rays passing through the image would reach the eye(represented by L)

looking towards the mirror.



g) Yes.

h) Yes, in the same way as an image is formed on a movie screen.

(This image could then be seen by the eye at M)

Fig 16


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8.






d) Would the image be visible to an eye located at L?...

e) Would the image be visible to an eye located at M?...

f) Would the image be visible to an eye located at N?...





Fig 17


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8.

a) Same size. Note that the object and image are at the same distance from the mirror

(twice the focal length).

b) Inverted.


d) Yes, light rays passing through the image would reach the eye at L.



g) Yes.

h) Yes, in the same way as an image is formed on a movie screen.

(This image could then be seen by the eye at M)

Fig 18


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9.






d) Would the image be visible to an eye looking towards the mirror as represented by L ?...







Fig 19


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9.

a) Larger.

b) Erect.

c) Virtual. In this case light reflected from the mirror and striking the eye located at L

would appear to come from the image I.

d) Yes, light rays apparently coming from the image would reach the eye at L.

e) No, the light rays described above would not reach the eye at M.

f) No, the light rays described above would not reach the eye at N.

g) No. As described earlier it is a virtual image.

h) No. There is no light present at the image I to form an image on a screen.

Fig 20


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10. Fig.21. shows an arrangement of a luminous object (a V-shaped lamp filament), a concave

mirror of 240 mm. focal length and a screen. The object and image distances are as shown and

are consistent with the ray diagram of Fig.22.

Fig 21

Fig 22

THIS QUESTION IS CONTINUED ON THE OPPOSITE PAGE AND ANSWERS ARE

GIVEN ON THE FOLLOWING TWO PAGES.


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a) Will the image be real or virtual?

Ans.....................

b) If the concave mirror were removed and replaced by a plane mirror what would be seen

on the screen?

A. No image.B. The image would remain unchanged.

C. An image brighter than the original.

D. An image dimmer than the original.

Ans...................

c) If the concave mirror is now replaced and its lower half is covered, what would be seen

on the screen?

A. No image.

B. The lower half of the image would disappear.

C. The upper half of the image would disappear.

D. The image would remain the same size but dimmer.Ans......................

d) If the screen were moved 100 mm.towards the mirror the image would

A. remain sharp but become smaller.

B. remain sharp but become larger.

C. disappear.

D. remain the same size but become slightly fuzzier.

Ans.................

e) If the screen were removed and you looked for an image by locating your eye at point X

in Fig.21. and looked towards the mirror, which of the following would describe what

you would see? (Use the ray diagram of Fig.22. to help decide.)

A. The image of the filament located at the position previously occupied by the

screen.

B. The image of the filament close to the actual lamp filament.

C. The image of the filament on the surface of the mirror.

D. It would not be possible to see an image.

Ans..................

f) With the screen still removed you locate your eye at the point Y of Fig.21. and look

towards X. What would you see?A. The image of the filament located at the position previously occupied by the

screen.

B. The image of the filament closer to you than the position previously occupied by

the screen.

C. The image of the filament further from you than the position previously

occupied by the screen.

D. It would not be possible to see an image.

Ans................

CHECK YOUR ANSWERS TO THIS QUESTION. REFER TO THE

APPROPRIATE SECTIONS OF YOUR TEXT BOOK FOR FURTHER

INFORMATION.


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10.

a) The image is a real one. Light actually passes through the image and indeed forms the

image where it strikes the screen.

b)

A is correct. The only image whichwould be seen would be the virtual image

located behind the plane mirror. The

rays from the filament are diverging. As

shown in Fig.23 it is only a concave

mirror which can reflect and focus them

into a converging beam which forms a

real image. After striking a plane mirror

the diverging rays still diverge and

appear to come from behind the mirror.

c)

D is correct. You may have been tempted to

say that the image was wholly or partly

obliterated because the rays shown in Fig.22.

would be blocked by covering the lower half

of the mirror. Remember however that these

rays are only two of many. Others are shown

in Fig.24. The image is of course dimmersince less light is involved in forming it.

Fig 23

Fig 24


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d) C is correct. With a simple optical system such as a concave mirror the image is in

sharp focus over a very small range of position i.e. for very small movements of the

screen. On moving the screen slightly the image becomes blurred and with larger

movements it disappears .

e)

A is correct. The image is a real one. Light passes through it. If the screen is not

present the light will continue on as shown in Fig.25. and enter your eye at X so that

you will see the image at its original location.

f) D is correct. Although your eye at Y is looking towards the image you would not be

able to see it since none of the light which forms the image enters your eye. It is all

directed away from the mirror. Replacing the screen would allow you to see the imagesince some of the light forming the image would bounce off the screen and enter your

eye.

TRY THESE EXPERIMENTS IN YOUR SCHOOL LABORATORY

Fig 25


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11.

The Figure shows fine beams of light striking anarrangement of small pieces of mirror. The

normals (perpendiculars) to these are shown

dotted. Draw in the reflected beams accurately

making use of the laws of reflection. Where do

these beams appear to come from?



12.

Consider now broad beams of light striking four

of the pieces of mirror. Draw in the reflections

of these beams. Where do these beams appear to

come from?



Fig 26

Fig 27


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This shows how parallel fine beams of light canbe made to diverge by using an arrangement of

small flat mirrors. Note that the beams appear to

be diverging from the point F.

12.

This shows how the beams have diverged.

Note that they do not appear to diverge from a

point as in the previous question but from a

region in the vicinity of this point.

Fig 28

Fig 29


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Interlude:

The two previous questions give a lead as to how to make a "diverging" mirror. If a mirror is

continuously curved rather than composed of small flat pieces it is possible to arrange for aparallel beam of light to diverge as if coming from a point.

Refer back to the Figures of the previous questions and think about the effect of replacing the

pieces of flat mirror with a smooth curve. This is shown in Fig.30. This shows the principle of

operation of a diverging mirror. Any ray parallel to the axis AB of this mirror will appear to

come from the point F, known as the principal focus. A small spherical mirror will behave

approximately in this way.

In the lower part of Fig 30 you can see that a light ray directed towards F such as the ray DC

will, after reflection, travel parallel to the axis AB. This is an illustration of the reversibility of

light rays i.e. if a light ray is "sent back on its tracks" it will follow the same path.

Fig 30


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It is usual in ray diagrams to represent the curved mirror by a single line (shown dotted in

Figure 31) and to make use of the construction that any ray parallel to the axis AB will be

reflected so as to appear to come from F and any ray directed towards F will after reflection be

directed parallel to AB. These are important rules for the construction of ray diagrams and thelocation of images using convex (diverging) mirrors. They are very similar to the rules

described earlier for use with concave (converging) mirrors.

Fig 31


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13.

The figure shows an arrangement of small plane mirrors struck by fine beams of light coming

from a luminous object O.

Draw in the reflected rays accurately using the laws of reflection.

Where do the reflected rays appear to come from ?

What is the nature (real or virtual) of the image at O ?



Fig 32


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13.

Light diverging from the object O is reflected and the reflected beams continue to diverge. Note

that they appear to come from the point I. Here again you could imagine the effect of replacing

the pieces of flat mirror with a curved mirror. All beams diverging from O would after

reflection appear to be coming from the point I. It would not be possible to form an image on a

piece of white paper placed at I. No light reaches this point. The image at I is a virtual image.

It is of the same nature as images formed with a flat mirror.

Fig 33


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14.

A luminous object is placed at the point O in front of a convex spherical mirror whose principal

focus is at F. Two rays are drawn from O, one parallel to the axis of the mirror and the otherpassing through the pole of the mirror P. These strike the mirror (represented by the dotted

line). Draw in the reflected rays and locate the image of the object O.



15.

Consider now an extended object, an arrow as indicated in the Figure. Rays are drawn from

two points on it. Complete the ray diagram and decide what form the image takes.



Fig 34

Fig 35


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14.

Ray OP will be reflected as shown at P and ray OD will be reflected so that it appears to be

coming from F. These will intersect at I, the image of O.

15.

The two points on the arrow are imaged as shown in the Figure so that the virtual image of the

arrow is the upright arrow shown. It is not necessary in a ray tracing exercise to locate the

images of a series of points on the object, one point, for example the tip of the arrow, is

sufficient.

Fig 36

Fig 37


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16.






d) Would the image be visible to an eye looking towards the mirror represented by

L? ...

e) Would the image be visible to an eye M looking away from the mirror ?...

f) Would the image be visible to an eye N looking behind the mirror ?...


h) Could the image be made visible on a screen (or a piece of white paper)?..........GO STRAIGHT TO THE NEXT THREE QUESTIONS. DON'T CHECK

YOUR ANSWER YET. WAIT UNTIL YOU ARE INSTRUCTED TO DO

SO.

17. Consider the same situation as in the previous question but with the object O in some

other position in front of the convex mirror. Which of your answers to the previous

question could be changed. Ans.......

18. Is it possible to form a virtual image further from the mirror than the point F ?.......

19. Is it possible to place an object in front of the mirror and form a real image ?.......

CHECK YOUR ANSWERS TO THIS LAST GROUP OF QUESTIONS. REFER TO

THE APPROPRIATE SECTIONS OF YOUR TEXT BOOK FOR FURTHER

INFORMATION.

Fig 38


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16.

a) Smaller

b) Erect.

c) Virtual, see also answer g).

d) Yes, light rays which appear to come from the image would reach the eye at L.

e) No, light rays appearing to come from the image would not reach the eye at M.

f) No, light rays appearing to come from the image would not reach the eye at N.

g) No.

h) No. Light rays do not actually pass through the image and so an image would

not form on a screen placed in the vicinity of I.

17. None of the answers would be changed. Ray tracing will show that the image of anyobject placed in front of a convex mirror will be smaller, erect and virtual.

18. No. Ray tracing from close or remote objects will verify this. No matter how close or

how distant the object is from the mirror the image will always be located between the

mirror and F.

19. No. Ray tracing will show that the rays reflected from the mirror are always diverging.

Thus the rays reaching the eye at L always appear to come from a point behind the

mirror (that is from a virtual image).

Fig 39


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03images and curved mirrors

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