A
short linear object of length L lies on the axis of a spherical
mirror, a distance o from the mirror. (a) We
have to show that its image will have a length
|
Solution: Click For PDF Version For answering this problem, we will use the mirror equation
In this
equation o is the
object distance,
We will find
the longitudinal magnification by calculating the difference between
the image distances of points at object distances
Therefore,
We obtain
As the object is assumed to be short, we use the approximation
and find
Therefore, the longitudinal magnification is
The lateral magnification m is
we note that
|
,
where
is equal to
,
where m is the lateral magnification.
.
is the image distance, and f
is the focal length which is one-half of the radius of curvature of
the mirror. We use the sign convention of the textbook Physics,
Halliday, Resnick and Krane.
and
.
From the mirror equation, we note that
.
