What is the optical separation interval of the two lenses?

 $\left( A \right)x \\
  \left( B \right){f_1} + {f_2} \\
  \left( C \right){f_1} + {f_2} - x \\
  \left( D \right){f_1} + {f_2} + x \\ $

Hint :This lens system is basically used to form an image of an object which is kept at a certain distance from the lens. In the given situation the size of the image formed does not depend upon the distance of the object according to the lens. Length OP is equal to the length OF as both is $ f2 $ . Similarly length O’F and length OF is equal to the focal length $ f1 $ .

Complete Step By Step Answer:
In order to solve this question we see that we have to find the optical separation level, that is PP’ in the figure. Now the distance between the two lenses is $ x $ .
Length OP is equal to the length OF as both is $ f2 $ . Similarly length O’F and length OF is equal to the focal length $ f1 $ .
Now total length OO’ is equal to $ x $ from the figure;
So,
 $ OO' = OP + PP' + O'P \\
   - x = {(f)_1} + PP' + ({f_2}) \\
  PP' = {(f)_1} + ({f_2}) - x \\ $
Hence, option C is the correct option.

Note :
Here both the focal lengths when taken inside the lenses are as negative so we take the OO’ length as negative. PP’ is the optical separation level which is between the focus of the length present here. The optical axes of the lenses coincide. This lens system is basically used to form an image of an object which is kept at a certain distance from the lens. In the given situation the size of the image formed does not depend upon the distance of the object according to the lens.