CONVEX MIRROR
Defn: Convex mirror is the curved mirror which curved inward.
Diagram: 1
CONCAVE
MIRROR
Defn: Concave mirror is the curved mirror which curved outward.
Diagram: 2
TERMS USED IN
THIS TOPIC
Consider the diagram below when two curved mirror joined
Diagram: 3
Where:
AB = Convex mirror
ST = Concave mirror
C = centre of curvature
L = pole of the Concave mirror
K = pole of the Convex mirror
CL = radius of curvature of the Concave mirror Ck = radius of
curvature of the Convex mirror
CL = principal axis of the Concave mirror
Ck = principal axis of the Convex mirror
Centre
of Curvature
Defn: centre of curvature is the centre of the sphere in which the
mirror is a part.
Radius
of Curvature of the Curved Mirror
Defn: radius of curvature of the curved mirror is the
distance/length between the pole of the curved mirror and the centre of
curvature.
Principal
Axis of the Curved Mirror
Defn: principal axis of the curved mirror is the line joining the
pole of the curved mirror and the centre of curvature.
Consider when the light reflected in the curved mirror as
shown in the diagram below.
Diagram: 4
Principle
Focus, F
Defn: Principle focus is the point in which the light is reflected
in curved mirror
Focal
Length, f
Defn: focal length is the length/distance between poles of curved
mirror to the principal focus
NB: it was proved
that focal length is equal to half of radius of curvature. f = π/π
LOCATION
OF IMAGE USING RAY DIAGRAMS
The following is the rules used to locate image in the curved
mirror.
i. A ray of
light travelling to the mirror parallel to the principal axis a ray is
reflected through the principal focus
ii. A ray of
light travelling to the mirror through the centre of curvature is reflected
along its own path
iii. A ray of light travelling to the mirror through the
principal focus is reflected parallel to the principal axis
Note: any two of these rays are sufficient to locate the image.
PROCEDURE
TO DRAW RAY DIAGRAM
The following procedure is used to draw accurate ray diagrams
to locate the image.
i. Choose an
appropriate scale so that the ray diagram fits on the available space.
ii. Draw a
horizontal line to represent the principal axis of the mirror. Mark the focal
point of the mirror.
iii. Using the
chosen scale, draw the object in position along the principal axis. The object
is drawn as a vertical line from the principal axis.
iv. Locate the
position of the image by drawing rays from the object to the mirror. Use the
rules for drawing ray diagrams to draw the reflected rays.
v. At the point of intersection of the reflected rays, draw
the image in position
Example, 01
An object 20cm high is placed 40cm from a concave mirror of
focal length 15 cm. determine the position, nature and size of the image formed
by drawing a ray diagram.
Solution:
Image
Formed In Curved Mirror
Terms used to describe images formed by curved mirrors:
Position
i. Real image
is on the same side of the mirror as the object.
ii. Virtual image is on the opposite side of the mirror
compared to the object.
Nature
iii. Upright
image has the same orientation as the object.
iv. Inverted image is oriented in an upside down position
compared to the object.
Size
v. Enlarged
image is bigger than the object.
vi. Diminished image is smaller than the object
Images
Formed By Concave Mirrors
The following are the characteristics of images formed by
concave mirrors:
Object
at Infinity (Very Far).
The image is formed at the focal point, F, of the mirror. It
is inverted, diminished and real.
Diagram: 5
Object
at the Centre of Curvature, C
The image is formed at C. It is real, inverted and the same
size as the object.
Diagram: 6
Object
beyond the Centre of Curvature, C
The image is formed between C and F. It is real, inverted and
diminished.
Objects between F and C
The image is formed beyond C. It is real, inverted and
magnified.
Diagram: 8
Object
at F
The image is formed at infinity.
Diagram:9
Object
between F and P
The image is formed behind the mirror and is virtual, erect
and magnified
Diagram: 10
Image
Formed In Convex Mirror
The images formed are always virtual, erect and diminished
for all object positions.
Diagram: 11
The
Mirror Formula
The mirror formula is expressed as follows:
NB:
i. Focal length,
(f) for a concave mirror is positive (+)
ii. Focal length
(f) for a convex mirror it is negative (-)
iii. the image
distance, (v) is negative (-) For a virtual image
iv. The image distance, (v) is positive (+) for real images
Magnification
of an Image
Defn: Magnification (M) is the ratio of the image size/ height (IH)
to the object size/height (OH)
Formula:
M =
HI/HO
Defn: Magnification is the ratio of the image distance (v) from the
mirror to the object distance (u) from the mirror
M = v/u
NB:
i. Magnification
has no units
ii. The image
formed by a curved mirror can be larger, smaller or the same size as the
object.
iii. When the
ratio is greater than one, the image is enlarged
iv. When the ratio is less than one, the image is diminish
Example, 02
An object 3 cm high is placed 30 cm away from a concave
mirror of focal length 12 cm. using the mirror formula, find the position, the
height and the nature of the image formed.
Data given:
Focal length, f =l2cm
Image distance, v =?
Object height, OH = 3cm
Object distance, u = 30 cm
Solution:
1st find distance of object
From:
=
make v subject
V = (uf)/u-f
V = (30x12)/ (30-12)
V = 360/18
V = 20 cm
The image is real
2nd find the image height, IH
From: M =
But: M =
Therefore:
=
- make IH subject
IH = (OH x v)/u
IH = (3 x 20)/30
IH = 60/30
IH = 2 cm
The image is diminished.
Example, 03
A concave mirror with a radius of curvature of 30 cm produces
an inverted image 4 times the size of an object placed on its principal axis.
Determine the position of the object and that of the image.
Data given:
Radius of curvature, r = 30
Focal length, f = r/2 = l2cm
Magnification, M = 4
Image distance, v = ?
Object distance, u = ?
Solution:
1st find distance of object
Form: M =
4 = π£π’ - make v
subject
v = 4u
Then: From:
=
make u subject
u = (vf)/v-f
Substitute v by putting 4u
u = (4ux f)/(4u-f)
u = (4ux 15)/(4u-15)
u = 60u/(4u-15) – multiply by (4u-15) both sides
u(4u-15) = 60u
4u2 -15u = 60u
4u2 = 60u + 15u
4u2 = 75u
4u = 75
u = 18.75 cm
2nd find image distance, v
From: 4u = 75 cm
But: 4u= v
Therefore v= 75 cm
v = 75 cm
Example, 04
An object 30 cm high is placed 20 cm away from a convex
mirror of focal length 25 cm. Describe the image formed.
Data given:
Focal length, f = -25cm
Object height, OH = 30cm
Object distance, u = 20 cm
Image distance, v = ?
Image height, IH = ?
Solution:
1st find distance of object
From: π/π = π/π + π/π make v subject
V = (uf)/u-f
V = (20x-25)/ (20--25)
V = (20x-25)/ (20+25)
V = -500/45
V = -11. cm
The image is virtual
2nd find the image height, IH
From: M = π°π―/πΆπ―
But: M = ππ
Therefore: π°π―πΆπ― = ππ - make IH subject
IH = (30 x -11.1)/20
IH = -333/30
IH = -16.8 - always is positive
IH = 16.8 cm
The image is diminished.
NB:
i. Convex
mirrors produce diminished images but have a very wide field of view compared
to plane mirrors
ii. Concave mirrors magnify images
Uses of Convex
Mirrors
The following are some of the areas where convex mirrors are
used:
i. Used in driving due to Wide field of view
ii. Seeing
around corners to avoid the crashing of vehicles or supermarket trolleys at the
corners
iii. Supermarket surveillance for surveillance in business
establishments and security installations
Uses of Concave Mirrors
The following are some of the areas where concave mirrors are
used:
1. Shaving
mirrors due to magnification and erect image
2. Reflecting telescopes
Diagram: 12
3. Used in solar
cookers.
4. It is used to making car headlamp and torch by concave
mirror called parabolic mirror
Diagram:13
