6. Problem solving - Reflection - Plane and Curved mirrors

Reflection - Problem Solving
Plane and Curved mirrors
Reflection Plane and Curved mirrors
Mirror Equation
1 1 2
R
+ = ; Focal length of a mirror f =
2
u v R
ALL distances are measured from the pole of the mirror.
For mirrors, the following results hold:
1. The object distance ‘u’ is negative (-ve), if the object is in front of the mirror (Real Object).
2. The object distance ‘u’ is positive (+ve), if the object is behind the mirror (Virtual Object).
3. The image distance ‘v’ is negative (-ve), if the image is in front of the mirror (Real Image).
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4. The image distance ‘v’ is positive (+ve), if the image is behind the mirror (Virtual Image).
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5. Focal length of a concave mirror is taken as negative (-ve).
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v
=−
ho
u
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Linear Magnification m =
n.
6. Focal length of a convex mirror is taken as positive (+ve).
7. When the image formed by a spherical mirror is real, it is also inverted and is on the same side of the mirror
as the object. Since both v and u are negative, the magnification is negative.
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8. When the image formed by a spherical mirror is virtual, it is also erect and is on the other side of the mirror
as the object. In this case, u is negative and v is positive, therefore, magnification is positive.
Position of the Object
Concave Mirror
Position of the Image
Nature of the Image
1. At infinity
At F or in the focal plane
Real, inverted and extremely
diminished in size.
2. Beyond C
Between F and C
Real, inverted and diminished.
3. At C
At C
Real, inverted and equal to the
size of the object.
4. Between C and F
Beyond C
Real, inverted and enlarged.
5. At F
At infinity
Extremely magnified
6. Between F and Pole
Behind the mirror
Virtual, erect and enlarged.
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S.No.
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respect to the object.
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9. If m is positive, the image is erect with respect to the object and if m is negative, the image is inverted with
Convex Mirror
7. At infinity
Appears at F
Virtual, erect and extremely
diminished.
8. Between infinity and pole
Appears between F and Pole
Virtual, erect and diminished.
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Reflection - Problem Solving
Plane and Curved mirrors
Exercise 1
1. A billiard ball and a basket ball are painted with a reflecting coating. Which has the greater focal length?
2. The image of the point object P in the diagram shown is viewed by an eye, as shown. Draw a bundle of rays
from the object that reflect from the mirror and enter the eye. For this object position and mirror, indicate the
region of space in which the eye can be positioned and still see the image.
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B
C
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A
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3. In the diagram shown, for which (one or more) of objects A, B, C, D and E can an observer at O see an
image in the plane mirror?
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4. A 0.12 m tall candle stands upright between two vertical plane mirrors A and B. The mirrors are parallel to
each other. The candle is 0.20 m from mirror A and 0.30 m from mirror B. (a) Find the positions of the two
nearest images of the candle in each mirror. (b) Find the height of each of the images.
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5. When two plane mirrors are parallel, such as on opposite walls in a barber shop, multiple images arise
because each image in one mirror serves as an object for the other mirror. A point object is placed between
parallel mirrors separated by 30 cm. The object is 10 cm in front of the left mirror and 20 cm in front of the
right mirror. (a) Find the distance from the left mirror to the first four images in that mirror. (b) Find the
distance from the right mirror to the first four images in that mirror.
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6. Can a virtual image be photographed? Explain.
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7. A person 1.62 m tall wants to see her full image in a plane mirror. (a) What must be the minimum height of
the mirror? (b) How far above the floor should the mirror be placed, assuming that the top of the person's
head is 15 cm above her eye level? Draw a ray diagram.
8. A candle 4.85 cm tall is 39.2 cm to the left of a plane mirror. Where is the image formed by the mirror and
what is the height of this image?
9. Find the position and height of the image formed by a concave spherical mirror with a radius of curvature of
0.40 m when a 0.10 m tall bottle stands 0.15m in front of the mirror.
10. A concave spherical mirror has a radius of curvature of 0.70 m. Find the position of the image formed for an
object placed at each of the following distances in front of the vertex of the mirror: (a) 0.20 m (b) 0.35 m (c)
0.70 m (d) ∞
11. Suppose the object in problem 11 is 0.10m tall, find the height of the image formed when the object is at
each of the positions in problem 11. Then in each of the four parts indicate whether the image is real or
virtual, upright or inverted, enlarged or reduced.
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Reflection - Problem Solving
Plane and Curved mirrors
12. Repeat problem 10 and 11 for the same given values if the mirror is convex rather than concave.
13. A concave spherical mirror has a radius of curvature of 24 cm. Draw ray diagrams to locate the image for an
object at a distance of (a) 55 cm, (b) 24 cm, (c) 12 cm, and (d) 8 cm from the mirror. For each case, state
whether the image is real or virtual; upright or inverted; and enlarged, reduced, or the same size as the object.
14. Repeat problem 13 for a convex mirror with the same radius of curvature.
15. A Concave mirror produces three times magnified real image of an object placed at 10 cm in front of it.
Where is the image located?
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16. We wish to obtain an erect image of an object, using a concave mirror of focal length 15 cm. What should be
the range of distance of the object from the mirror? What is the nature of the image? Is the image larger or
smaller than the object? Draw a ray diagram to show the image formation in this case.
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17. An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm. Find the position and
the nature of the image.
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18. An object 5 cm in length is placed at a distance of 20 cm in front of a convex mirror of radius of curvature 30
cm. Find the position of the image, its nature and size.
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19. An object of size 7 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance
from the mirror should a screen be placed so as to obtain a sharp image of the object? Find the size and the
nature of the image.
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20. (a) State the relation between object distance, image distance and the focal length of a spherical mirror.
(b) Draw a ray diagram to show the image formed by a concave mirror when an object is placed between the
pole and focus of the mirror.
(c) A concave mirror of focal length 15 cm forms an image of an object kept at a distance of 10 cm from the
mirror. Find the position, nature and size of the image formed by it.
[AISSE – 2006]
21. (a) Define real image of an object.
(b) Name the mirror that:
(i) can give real as well as virtual image of an object.
(ii) will always give virtual image of same size of an object.
(iii) will always give virtual and diminished image of an object.
(iv) is used by a doctor in examining teeth.
(c) With the help of a ray diagram explain the use of concave mirror as solar concentrators.
[SA II – 2011]
22. (a) For the given data showing object distance and focal length of three concave mirrors, answer the
following questions:
Object
S.No.
Focal length
distance
1.
30
20
2.
10
15
3.
20
10
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Reflection - Problem Solving
Plane and Curved mirrors
(i)
(ii)
(iii)
Out of the three in which case the mirror will form the image having same size as the object?
Which mirror is being used as a make-up mirror?
Draw the ray diagrams for part (i) and (ii).
(b) No matter how far you stand from the mirror, your image always appears erect and diminished. Identify
the type of mirror.
[SA II – 2011]
23. (a) Define principal focus of a spherical mirror.
(b) For what position of the object does a concave mirror form a real, inverted and diminished image of the
object? Draw the ray diagram.
(c) An object 4 cm high is placed at a distance of 6 cm in front of a concave mirror of focal length 12 cm.
Find the position of the image formed.
[SA II – 2011]
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24. The focal length of a concave mirror is 30 cm. Find the position of the object in front of the mirror so that the
image is three times the size of the object.
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25. An object is placed 15 cm from a concave mirror of radius of curvature 60 cm. Find the position of image
and its magnification.
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26. A 4.5cm needle is placed 12cm away from a convex mirror of focal length 15 cm. Give the location of the
image and its magnification.
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27. An object, 4.0 cm in size, is placed 25.0 cm in front of a concave mirror of focal length 15.0cm. At what
distance from the mirror should a screen be placed in order to obtain a sharp image? Find the nature and the
size of the image.
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28. A convex mirror used on an automobile has 3 m radius of curvature. If a bus is located at 5 m from this
mirror, find the position, nature and size of the image.
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29. (a) A concave mirror produces three times enlarged image of an object placed at 10 cm in front of it.
Calculate the focal length of the mirror.
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(b) Show the formation of the image with the help of a ray diagram when object is placed 6 cm away from
the pole of a convex mirror.
[SA II – 2012]
30. An object 1 cm tall is placed at a distance of 15 cm from a concave mirror of focal length 10 cm. Find the
position, size and nature of the image formed.
[SA II – 2013]
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