Mirror Formula and Magnification Video Lecture - Class 10

magnification and mirror formula you
know that concave mirrors are mainly
used for getting the enlarged images of
the objects convex mirrors are used for
getting the diminished image of a big
object while designing the mirrors we
need to know what is the size and
position of the images produced by it
for example the rearview mirror of a car
and the surveillance mirror in a
supermarket a convex mirrors but since
the area to be reflected by the rearview
mirror of a car is much larger than that
of the surveillance mirror of a
supermarket the radius of curvature of
these mirrors is different in this
session we will learn about
magnification and the factors affecting
magnification in spherical mirrors you
understand the image formation in
spherical mirrors we need to know the
new Cartesian sign conventions they are
the object is always placed to the left
of the mirror that is light from the
object falls on the mirror from the left
hand side all distances parallel to the
principal axis are measured from the
pole of the mirror all distances
measured to the right of the origin pole
are taken as positive and the distance
is measured to the left are taken as
negative Heights measured perpendicular
to and above the principal axis are
taken as positive Heights measured
perpendicular to and below the principal
axis are taken as negative let us also
understand a few definitions object
distance U the distance of the object
from the pole of the mirror is called
the object distance image distance
feel the distance of the image from the
pole of the mirror is called image
distance focal length M the distance of
the principal focus from the pole of the
mirror is called the focal length this
is half the radius of curvature of the
mirror the exact distance of the image
from the pole of the mirror can be gored
by the mirror formula 1 by u plus 1 by V
equals 1 by F the equals UF by u minus F
magnification produced by a spherical
mirror gives the relative extent to
which the image of an object is
magnified with respect in the object
size
it is given by the ratio of the height
of the image to the height of the object
it is expressed by the letter M
magnification is also expressed by the
ratio of image distance to that of the
object distance the height of the object
is taken as positive as the object is
usually placed above the principal axis
the height of the image is taken as
positive for virtual images and the
height of the image is taken as negative
for real images a negative sign in the
value of magnification indicates that
the image is real whereas a positive
sign in the value of magnification
indicates that the image is virtual
these mirror formulas are valid for all
positions of the object they are valid
for both concave and convex mirrors
take the concave mirror with the radius
of curvature as ten centimeters they
turn all with a height of 8 centimeters
place the doll at a distance of 15
centimeters from the mirror if the
radius of curvature is 10 centimeters
the focal length is half of it that is 5
centimeters as per the mirror formula 1
by 15 plus 1 by P equals 1 by 5 V equals
15 into 5 by 15 minus 5 which equals 7
point 5 centimeters the size of the
image formed can be determined by the
magnification formula which is M equals
H dash by H equals minus V by u H dash
equals minus V by u into H equals minus
7.5 by 15 into 8
equals minus four centimeters the
negative sign here means that the image
is real for a virtual image the height
would be positive the right of the
object is 8 centimeters and height of
the image is 4 centimeters hence the
magnification done by the Miller M is
0.5 but this the image is diminished by
50% from this demonstration we
understood the following formula where a
formula 1 by u plus 1 by V equals 1 by M
magnification in a mirror M equals H -
by H or - V by u now let's understand
the effect of radius of curvature on
image position and image size in a
concave mirror observe the position size
and nature of the image as the radius of
curvature changes