sign convention for the parameters related to the mirror equation
1. All distances should be measured from the pole.
2. The distances measured in the direction of incident light, to be
taken positive and those measured in the direction opposite to
incident light to be taken negative.
3. Height of object (ho
) and height of image (hi
) are positive if
measured upwards from the axis and negative if measured
downwards.
Now let us understand magnification, i.e. the relation between the size
of the object and the size of the image.
Magnification
(m)
The image formed by a spherical mirror varies
in size, here we discuss the variation in height only.
Observe figure 22.
A ray coming from OI
is incident at pole with
an angle of incidence 0, and get reflected with
same angle 0.
From fig. 22 we can say that ΔPOO'
and ΔPII'
are similar triangles. So
II'/00'=pI/p0
/OOI
= PI/PO ................(1)
according to sign convention
PO = –u; PI = –v; OOI
= h0
; II'
= –hi
Substuting the above values in equation (3).
-hi/ho = -v/-u
hi/ho= -v/u
∴ Magnification m =
hi/ho=-v/u
We define the magnification,
m = height of image(hi
)/
height of object (ho
)
In all cases it can be shown that
m = – image distance (v)/ object distance (u)
Calculate the magnifications with the information you have in table-
2, for all the five cases.
Example
An object 4cm in size, is placed at 25cm infront of a concave mirror
of focal length 15cm. At what distance from the mirror wmirror whould a screen
be placed in order to obtain a sharp image?Find the nature and the size of the mirror