Spherical Lenses

Image can be formed on the screen if it is real. Real image of
reduced size can be formed by a concave mirror or a convex
lens.
A diminished real image is formed by a convex lens when the
object is placed beyond 2 f and the image of such object is
formed between f and 2 f on other side.
Thus,
or 0. 1 m
or 0.25 m

For a lens
For a concave lens,/and u are negative, i.e. v will always be
negative and image will always be virtual.
For a mirror:

Here, / is positive and u is negative for a convex mirror.
Therefore, v is always positive and image is always virtual.

In general spherical aberration is minimum when the total
deviation produced by the system is equally divided on all
refracting surfaces. A planoconvex lens is used for this
purpose. In order that the total deviation be equally divided
on two surfaces, it is essential that more parallel beam (or the
incident and refracted) be incident on the convex side. Thus,
when the object is far away from the lens, incident rays will
be more parallel than the refracted rays, therefore, the object
should face the convex side,but if the object is near the lens,
the object should face the plane side. This has been shown in
figure.

Let focal length of convex lens is + f then focal length of
concave lens would be
From the given condition.


Therefore, focal length of convex lens = + 10 cm
and that of concave lens =- 15 cm
Correct answer is (d).

Focal length for the lens is given by,

After silvering the plane surface of the lens it converts to the thin plano convex mirror. focal length is now change. For mirror focal length is given by,
Thus, for the mirror eq is,
Where distance of the object from the mirror ,
and distance of the image from the mirror
Thus, substituting the values of and

minus sign indicates that it is to the left of the system.

From the lens formula,
we have,

Further,
(from the graph)
Now, differentiating the lens formula, we have


Substituting the values, we have