In this sub topic we will study two types of curved
mirror include:
i)
Convex /diverging mirror
ii)
Concave/converging mirror
CONVEX MIRROR
Convex mirror is the curved mirror which curved
inward.
Diagram:
Concave mirror is the curved mirror which curved
outward.
Diagram:
Consider the diagram below when two curved mirror joined
Diagram:
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
Centre of curvature is the centre of the sphere in which
the mirror is a part.
Radius of
Curvature of the Curved Mirror
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
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:
Principle focus is the point in which the light is
reflected in curved mirror
Focal Length, f
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 = 𝒓⁄𝟐
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 1
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:
1 cm represent 5 cm
According to scale;
Object size (OH) = 2 cm
Focal length (F) = 3 cm
Radius of curvature (R) = 6 cm
Object distance (U) = 8 cm
From the scale
above;
Image distance (V) = (4.8 x 5) cm = 24 cm
The image distance is 24 cm
Nature of the image
i)
Real
ii)
Inverted
Size of image
From the scale
above;
Image size (IH) = (1.2 x 5) cm = 6 cm
The image size is 6 cm
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 Enlarged image is bigger than the object.
v) 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:
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:
Diagram:
The image is formed between C and F. It is real, inverted
and diminished.
Diagram:
The image is
formed beyond C. It is real, inverted and magnified.
Diagram:
The image is formed at infinity.
Diagram:
The image is formed behind the mirror and is virtual,
erect and magnified
Diagram:
The images formed are always virtual, erect and
diminished for all object positions.
Diagram:
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 (-) the image distance, (v) is negative (-) For a
virtual image
iii) The image distance, (v) is
positive (+) for real images
Magnification of an Image
Magnification (M) is the ratio of the image size/ height
(IH) to the object size/height (OH)
Formula:
Magnification is the ratio of the image distance
(v) from the mirror to the object distance (u) from the mirror
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 diminished
Example 2
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.
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