Question

The optical axis of a thin equiconvex lens is the x-axis. The coordinates of a point object and its Image are (-40 cm, 1 cm) and ( 50 cm, -2 cm) respectively. Lens is located at-
A. $x = 20cm$
B. $x = - 30cm$
C. $x = - 10cm$
D. Origin

Answer 1

Hint: In case of lens usually there are two types used. Concave lens and convex lens. All will serve different purposes. Properties of different lenses are different. In case of concave lenses they always form virtual images. While convex lenses form both virtual and real images. Inverted image in the sense it is real.
Formula used:
$\eqalign{
  & \left| m \right| = \dfrac{{{h_i}}}{{{h_o}}} \cr
  & \left| m \right| = \dfrac{v}{u} \cr} $

Complete step by step solution:
Biconvex lens means the two surfaces of the lens are convex. There is a plano convex lens which means one side of the lens is planar and the other side of lens is convex.
In the given question, the height of the image is 2 centimeter and the height of the object is 1 centimeter.
$\eqalign{
  & \Rightarrow \left| m \right| = \dfrac{2}{1} \cr
  & \therefore \left| m \right| = 2 \cr} $
Let the mirror be ‘x’ distance from the origin.
$\left| m \right| = \dfrac{v}{u}$
‘v’ is the image distance from the lens and ‘u’ is the object distance from the lens.
So the image distance will be 50+x and the object distance will be 40-x.
By applying the same magnification formula again we get
$\left| m \right| = \dfrac{v}{u}$
$\eqalign{
  & \Rightarrow 2 = \dfrac{{50 + x}}{{40 - x}} \cr
  & \therefore \left| x \right| = 10cm \cr} $
Lens is at 10 centimeter towards the left from the origin.
So $x = - 10cm$

Hence, option C is the correct answer.

Note:
Concave mirror can be analogous to a convex lens. All the properties of image formed by the concave mirror will be possessed by the image formed due to convex lens. The only difference between the two images will be the side where images are formed. If images are formed on the object side in a concave mirror then images will be formed on the other side of the convex lens. Rest everything will be the same for the same position of objects in both the cases. Same can be applied for convex mirrors and concave lenses.