Sign convention for reflection by spherical mirrors Mirror formula and magnification
Sign convention for reflection by spherical
mirrors
To deal with the reflection of light by spherical mirror,
we have to follow a set of conventions is known as the new cartesian sign
convention.
The pole of the spherical mirror is taken as the origin.
The principal axis of the spherical mirror is taken as the
X-axis of the coordinate system.
The object is always placed to the left of the spherical mirror.
It means to say that the ray of light coming from the object falls on the
spherical mirror from the left handed side.
All the distances parallel to the principal axis are
measured from the pole of the spherical mirror.
All the distances which are measured to the right (along
+ve X-axis) are taken as the positive.
All the distance which are measured to the left of the
origin (along -ve X-axis ) are taken as the negative.
The height measured perpendicular to the principal axis and
are upward to the principal axis (along +ve Y-axis) are taken as positive.
The height measured
perpendicular to the principal axis and are downward to the principal axis
(along -ve Y-axis) are taken as negative.
Sign convention for reflection by concave mirrors
The object is always placed to the left of the mirror. It means to say that the ray of light coming
from the object falls on the concave mirror from the left handed side. Hence object
distance is taken as negative.
The centre of curvature lies in front of the concave
mirror, hence radius of the curvature are taken as negative in the case of the
concave mirror.
The focus lies in front of the concave mirror, hence the
focal length (f) are taken as negative in the case of the concave mirror.
When the image is formed , then All the distances which are
measured to the right (along +ve X-axis) are taken as the positive.
When the image is formed , then All the distance which are
measured to the left of the origin (along -ve X-axis ) are taken as the
negative
If the image is above the principal axis , then the image
height will be positive. It means image
is erect.
If the image is above the principal axis then the image
height will be negative . it means the image is inverted.
Sign convention for reflection by convex mirrors
The object is always placed to the left of the mirror. It means
to say that the ray of light coming from the object falls on the convex mirror
from the left hand side. Hence object distance is taken as negative.
The centre of curvature lies behind the convex mirror ,
then the radius of the curvature are taken positive.
The focus of the convex mirror lies behind the convex
mirror then the focal length of the convex mirror is taken as positive.
The image is always formed behind the mirror in the case of
the convex mirror. Hence the distance of the image formed is taken as positive.
The image formed is always erect in the case of the convex
mirror. Hence, the height of the image formed is taken as positive.
Mirror formula
and magnification
Mirror formula states that there is a relationship between the
object distance (u) , image distance (v) and the focal length (f). all distance
are measured from the pole of the mirror.
Object distance (u) :--
In the
spherical mirror, The distance of the
object from its pole is called as object distance.
Image distance (v) :--
In the
spherical mirror, the distance of the image from its pole is called image
distance.
Focal length (f) :--
The distance of the
principal focus from the pole of the mirror is called the focal length.
The mirror formula is
expressed as:--
1/v
– 1/u =
1/f
Magnification
:--
Magnification produced by the spherical mirror is expressed as the
ratio of the height of the image to the height of the object.
Magnification
is denoted by the letter (m).
Height
of the object is h
Height
of the image is h’
The
magnification (m) produced by the spherical mirror is given by :--
Height of the image (h’)
Magnification
(m) = ........................................
Height
of the object (h)
h’
M
= …....
h
The magnification (m) is also related to the object
distance (u) and image distance (v).
This relationship is also expressed as :-
h‘ v
Magnification (m) =…………… = - ………
h u
-ve (negative sign indicated that the image is real.
And the positive sign (+ve) indicated as the image is virtual.
Tabular form for different position of spherical mirror:--
|
Types of the mirror |
Position of the
object |
Image distance |
Focal length(f) |
Height of the object |
Magnification (m) |
Height of the image |
|
Concave mirror |
Between P&F |
+ve |
-ve |
+ve |
-ve |
+ve |
|
Concave mirror |
Between F&c |
-ve |
-ve |
+ve |
-ve |
-ve |
|
Concave mirror |
At C |
-ve |
-ve |
-ve |
-ve |
-ve |
|
Concave mirror |
Beyond the C |
-ve |
-ve |
+ve |
-ve |
-ve |
|
Convex mirror |
In font of it |
+ve |
+ve |
+ve |
-ve |
+ve |
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