Q. A convex lens forms a real and inverted image of a needle at a distance of 50 cm from it. Where is the needle placed in front of the convex lens if the image is equal to the size of the object? Also, find the power of the lens.
Answer:
v  =  50 
m  =  1 
1  
P  = 

= ?  
f 
As the image formed by lens is real
v  
m  = 


u  
v  
1  = 


u  
v  =  u  
u  =  −  50 cm 
∴ Object distance is = 50 cm
1  1  1  

− 

= 


v  u  f  
1  1  1  

− 

= 


50  − 50  f 
1 + 1  1  

= 


50  f  
2 f  =  50  
f  =  25 cm = .25 m 
1  100  
P  = + 

= + 

=  + 4 dioptre  
.25  25 
The power of convex lens is + 4 dioptre