Two thin lenses, both of 10 cm focal length—one convex and other concave, are placed 5 cm apart. An object is placed 20 cm in front of the convex lens. Find the nature and position of the final image.

For refraction at the convex lens, we have
u = –20 cm; f₁ = 10 cm; v = v₁ = ?
Using lens formula, we have
                          
                          

The convex lens produces converging rays trying to meet at I₁, 20 cm from the convex lens, i.e., 15 cm behind the concave lens.
I₁ will serve as a virtual object for the concave lens.
For refraction at the concave lens, we have

For concave lens
                            
                              
As per sign convention
                                
                                 
                                  
                                             
       
         
i.e., This image is in the side of object 5 cm Right to concave and 10 cm (5 + 5) from convex
u = + 15 cm; v =?, f = –10cm Using lens formula, we have
               
                     
Hence, the final image is virtual and is located at 30 cm to the left of the concave lens.