An eye can distinguish between two points of an object if they are separated by more than 022mm when the object is placed at 25 cm from the eye. The object is now seen by a compound microscope having a 20 D objective and 10 D eyepiece separated by a distance of 20 cm. The final image is formed at 25 cm from the eye. What is the minimum separation between two points of the object which can now be distinguished?

Given data -Power of the objective lens = 20 D


Separation between the objective and the eyepiece = 20 cm


For clear vision the least distance, D = 25 cm


For eyepiece-


Power of the eyepiece = 10 D


The focal length of the eyepiece is given by





To distinguish the two points having minimum separation, the magnifying power should be maximum-Image distance,



Focal length



Objective lens-


The focal length of the objective lens is given by





Using lens formula for the objective lens and using eyepiece image distance , we have–






Given that, the objective is placed at a distance of 20cm from the eyepiece .


For calculating the image distance, for lens, using lens formula-






Applying lens formula for objective-





Now, lets calculate the magnification of the compound microscope –





Hence the minimum separation between two points of the object which can now be distinguished


by eyes becomes –



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