An angular magnification (magnifying power) of 30X is desired using an objective of focal length 1.25cm and an eyepiece of focal length 5cm. How will you set up the compound microscope?

Explanation

`rArr` In normal arrangement of microscope, image is obtained at normal vision distance. Hence,
D= 25 c, `f_e= 5 cm` angular magnification of eye- piece `1 + (D)/(f_e) = 1 + (25)/(5) =6`
`rArr` Overall magnification of microscope,
`m = m_e xx m_0`
`therefore m_0 = (m)/(m_e) = 30/6 = 5`
`therefore (v_0)/(u_0) = -5` [ For real image ]
`v_0 = - 5u_0 and f_0 = 1.25 cm`
`rArr ` Now, lens formula,
`1/f_0 = 1/v_0 - 1/u_0`
`therefore 1/f_0 = (-1)/(5u_0) - (1)/(u_0) = (-6)/(5u_0)`
`therefore 5u_0 = -6 f_0 = -6 xx 1.25`
`therefore u_0 = (-7.5)/(5) = 1.5 cm `
Hence, object should be at 1.5 cm away from objetive
`therefore v_0 = -5u_0 = - 5 xx (-1.5) = 7.5 cm `
`rArr` Now, for eye, piece `v_2 = -25` cm and `f_e = 5cm `
`therefore` Lens formula.
`1/f_e = (1)/(v_2) - (1)/(u_2)`
`therefore (1)/(u_2) = (1)/(v_2) - (1)/(f_e)`
`therefore (1)/(u_2) = - (1)/(25) - (1)/(5) = -(6)/(25)`
`therefore u_2 = - (25)/(6) = - 4.17 cm `
` therefore ` In compund microscope distance between objective and eye- piece,
`=| u_2| + |v_2|`
`4.17 + 7.5`
`= 11.67 cm`