1. PHYSICS InClass by SSL Technologies with S. Lancione Exercise-48
High School
InClass
by SSL Technologies
with S. Lancione
Exercise-48
Curved mirrors
Part 1 /2

2. Curved mirrors PART-1 /2 Study the terminology of parabolic mirrors.
Light rays
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3. Curved mirrors RULES FOR DRAWING RAYS IN CURVED MIRRORS
A ray that is parallel to the principal axis is reflected through
the principal focus (F).
A ray passing through the principal focus (F) is reflected parallel
to the principal axis.
A ray passing through the center of curvature (C) is reflected
back along its own path.
Note that images have properties called "characteristics".
Image characteristics include:
Location of image (behind mirror or in front of mirror)
Size (magnification) of image (larger or smaller than object)
Attitude (whether the image is inverted or upright)
Reversed (whether the image is reversed left-to-right, "mirror image")
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4. Be sure to study each case!
Concave mirrors
 CONCAVE MIRRORS
The characteristics of an image formed by a concave mirror depend
on the location of the object. As it turns out, there are six “strategic”
locations where an object may be placed. For each location, the
image will be formed at a different place and with different
characteristics. We will study the six different locations and label them as CASE-1 to CASE-6. 6
Be sure to study each case!
Case-1: Object at infinity
Case-2: Object just beyond C
Case-3: Object at C (center of curvature)
Case-4: Object between C and F
Case-5: Object at F (focal point)
Case-6: Object between F and V (within focal length)
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5. In order to draw images formed by curved mirrors, remember that :
A ray parallel to the principal axis is reflected through the focal point (F).
MEMORIZE THIS! F C
Principal axis
Back of
mirror V
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6. In order to draw images formed by curved mirrors, remember that :
A ray that goes through the focal point (F) is reflected parallel to the principal axis.
MEMORIZE THIS! F C
Principal axis
Back of
mirror V
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7. In order to draw images formed by curved mirrors, remember that :
A ray that strikes the vertex (V) is reflected like a plane mirror. (Angle of incidence = Angle of reflection)
MEMORIZE THIS! F C
Principal axis
Back of
mirror
Incident ray
Incident ray V
Reflected ray
Reflected ray
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8. A ray that goes through C
In order to draw images formed by curved mirrors, remember that :
A ray that goes through C
(the center of curvature) is reflected back along its own path.
MEMORIZE THIS! F C
Principal axis
Back of
mirror V
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9. Concave mirrors Important f
This distance is known as the “focal length” (f). f
REMEMBER
The focal length (f) is from the focal point (F) to the vertex point (V).
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10. Concave mirrors Object at infinity No image
Due to the great distance the object is from the mirror,
all rays arrive at the mirror parallel to the principal axis.
As a result, all rays focus at the focal point and no image
is formed.
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11. Image is real, between C and F, inverted and reduced.
Concave mirrors
Object just beyond C
Image is real, between C and F, inverted and reduced.
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12. Image is real, located at C, inverted and same height as object.
Concave mirrors
Object at C
Image is real, located at C, inverted and same height as object.
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13. Image is real, located beyond C, inverted and larger than the object.
Concave mirrors
Object between C and F
Image is real, located beyond C, inverted and larger than the object.
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14. All rays are reflected parallel and thus no image is formed.
Concave mirrors
Object at F
All rays are reflected parallel and thus no image is formed.
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15. Object between F and V (within the focal length)
Concave mirrors
Object between F and V (within the focal length)
Image is virtual, located inside the mirror, upright and larger than the object.
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16. Like this Like this C C F Object Image We can now draw the image.
Object point
An object is placed in front of a concave mirror.
Find the location and
characteristics of the image.
TASK
Such as right here!
Rather than draw an actual
object, it is easier to draw
the object as an arrow. This way, we can tell if the image is inverted or not.
Incident ray
Incident ray
Object C
Since we are not given the location of the object,
we can select any arbitrary location.
Objects consist of an infinite number of points.
And each point has an infinite number of rays radiating outwards.
Images also consist of an infinite number of points.
Each point on the object has a corresponding point on the image.
In locating an image, we take one point on the object and find its corresponding point (location) on the image object.
As shown above, we usually take the (extreme) top point
and find its corresponding point on the image object. C F
Image
We can now draw the image.
Image point
Reflected ray
Back of
mirror
Where the two reflected rays meet is the image point of the object point.
NOTE
Reflected ray
Characteristics of the image
~ Real (formed by reflected rays)
~ Inverted (upside down)
~ Smaller than the object
There are two steps in finding the image of a concave mirror.
Draw a ray through the focal point and make it reflect parallel to the principal axis.
Step-2
Draw a ray parallel to the principal axis and make it reflect through the focal point.
Step-1
Since the intersecting rays are both reflected rays,
the image is real.
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17. Convex mirrors produce a very large field of view.
NOTE
For convex mirrors, the image is always virtual, always located inside the mirror, always upright and always smaller than the object.
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18. EXERCISES

19. Question-1
State the rules for finding the image formed by a curved mirror.
1- A ray parallel to the principal axis is reflected through the
focal point (F).
2- A ray through the focal point (F) is reflected parallel to the
principal axis.
3- A ray through the center of curvature (C) is reflected back along its own path.
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20. Question-2 State four characteristics of images.
1- Type (real or virtual)
2- Location (distance from mirror)
3- Magnification (size)
4- Attitude (upright or inverted
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21. Question-3 What is spherical aberration and how can it be eliminated?
A fuzzy image produced by the fact that parallel rays do not pass through the focal point (F).
It can be eliminated by making the mirror parabolic rather than spherical.
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22. Question-4 Focal plane Principal axis Vertex (V) Reflected ray
The diagram below displays a concave mirror and a beam of light
striking the mirror. Label each part.
Focal plane
Concave mirror
Principal axis
Vertex (V)
Reflected ray
Focal point (F)
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23. Question-5 Extended ray Incident ray Reflected ray
The diagram below illustrates the image of an object produced
by a concave mirror. Label the incident ray, the reflected ray
and the extended ray.
Extended ray
Incident ray
Reflected ray
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24. (formed by reflected rays)
Question-6
For each concave mirror below, draw the image. a)
Image
Image is real
(formed by reflected rays)
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25. (formed by reflected rays)
Question-6
For each concave mirror below, draw the image. b)
Image
Image is real
(formed by reflected rays)
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26. (formed by reflected rays)
Question-6
For each concave mirror below, draw the image. c)
Image
Image is real
(formed by reflected rays)
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27. (formed by extended rays)
Question-6
For each concave mirror below, draw the image. d)
Image
Image is virtual
(formed by extended rays)
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28. The focal point (F) is half the radius of curvature (C).
Question-7
The diagram below shows an illuminated object and its virtual image in a concave parabolic mirror.
Determine the location of the focal point (F). F C
REMINDER
The focal point (F) is half the radius of curvature (C).
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29. Image is virtual, upright and smaller than the object.
Question-8
The diagram below shows an object in front of a convex parabolic mirror. Draw the image.
Image is virtual, upright and smaller than the object.
Image
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30. Question-9
Where must an object be placed in front of a concave mirror so as to form an image that is:
a) Smaller than object? ____________________________________
b) Inverted? ____________________________________
c) Virtual? ____________________________________
d) Inverted and magnified ? ____________________________________
e) Same height as object? ____________________________________
Just beyond the center of curvature (C).
Beyond the focal point (F).
Within the focal length (f).
Between C and F.
At the center of curvature (C).
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31. Question-10
Consider a convex mirror, where must an object be placed so as produce a real image?
Impossible, convex mirrors do not produce real images.
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32. Question-11 State the properties of a virtual image.
A virtual image is formed by extended rays.
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33. Question-12
In what important way does a virtual image differ from a real image?
In the fact that a virtual image cannot be projected onto a screen.
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34. Question-13
Consider an object placed in front of a concave mirror. Which one of the following statements correctly describes its image?
Back
Image
A) It is in front of the mirror, inverted, real and smaller than the object.
B) It is behind the mirror, upright, virtual, and smaller than the object.
C) It is in front of the mirror, upright, real and smaller than the object.
D) It is behind the mirror, upright, virtual and larger than the object.
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35. Question-18
An object is placed in front of a convex mirror as illustrated below.
Draw and label the light rays necessary to locate the image.
Reflected ray
Incident ray
Extended ray
Incident ray
Image
Extended ray
Reflected ray
Image is virtual, upright and reduced.
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