An optical instrument used for angular magnification has a 25 D objective and a 20 D eyepiece. The tube length is 25 cm when the eye is least strained. (a) Whether it is a microscope or telescope? (b) What is the angular magnification produced?

Answer

B, C

Explanation

Micrioscope For given microscope,
`f_(upsilon) = (1)/(25D) = 0.04m = 4 cm,`
`f_e = (1)/(25D) = 0.05m = 5 cm.`
Tube, length = 25 cm, `upsilon_e = 25 cm.`
`:. (1)/(upsilon_0) - (1)/(u_e) = (1)/(f_e)`
`-(1)/(25) - (1)/(u_e) = (1)/(5)`
`rArr - (1)/(u_e) = (1)/(5) + (1)/(25) = (5+1)/(25) = (6)/(25)`
`rArr u_e = - (25)/(6)cm`
`:. upsilon_0 = 25 - (25)/(6)`
`=25xx (5)/(6) = 20.84cm.`
`Again, `(1)/(upsilon_0) - (1)/(u_0) = (1)/(f_0)`
`(1)/(20.83) - (1)/(u_0)= (1)/(4)`
`rArr - (1)/(40) = (1)/(4) = (1)/(20.84)`
`=(5.21 -1)/(20.84) = (4.21)/(20.84)`
`rArr - (upsilon_0)/(f_0) = 4.21`
So, required magnification (m)
`= (upsilon_0)/(u_0) ((D)/(f_e)) = 4.21 xx (25)/(5) = 21.`