An eye can distinguish between two points of an object if they are separated by more than 0.22 mm 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?

Answer

D

Explanation

For the given compound microscope, `f_0 = (1)/(20) D = 0.05m - 5 cm,`
`f_e = (1)/(10)D = 0.1 m =10 cm`
D = 25 cm, seperation between objective and eyepiece = 20 cm For the minimum seperation between two points which can be distinguished by eye using the miscroscope, the magnifiying power should maximum. For the eyepiece.
`upsilon_e = -25 cm f_e = 10 cm`
So, ` (1)/(u_e) = (1)/(upsilon_e) - (1)/(f_e)`
` =(1)/(-25) - (1)/(10) = -(2+5)/(50)`
`rArr u_e = (-50)/(7) cm`
So the image distance for the objective lens should be,
`upsilon_0 = 20 - (50)/(7) = (90)/(7)cm`
Now, for the objective lens,
`(1)/(u_0) = (1)/(upsilon_0) - (1)/(f_0)`
`=(7)/(90) - (1)/(5) = (7-18)/(90) =- (11)/(90)`
`rArr u_0 = (-90)/(11)cm`
`m =(upsilon_0)/(u_0) (1+ (D)/(f_e))`
`=((90)/(7))/((-90)/(11)) (1+ (25)/(10))`
`=(11)/(7)xx (3.5) = 5.5`
Thus, minimum separation that the eye can distinguish `= (0.22)/(5.5) mm = 0.4 mm.`