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A compound microscope uses an objective ...

A compound microscope uses an objective lens of focal length `4 cm` and eye lens of focal length `10 cm`. An object is placed at `6 cm` from the objective lens. Calculate magnifying power of compound microscope if final image is formed at the near point. Also, calculate length of the tube of compound microscope.

Text Solution

Verified by Experts

Here, `f_(0) = 4cm, f_(e) = 10 cm`,
`u_(0) = -6cm, v_(e) = d = -25 cm`
From `(1)/(v_(0)) - (1)/(u_(0)) = (1)/(f_(0))`
`(1)/(v_(0)) = (1)/(f_(0)) + (1)/(u_(0)) = (1)/(4) - (1)/(6) = (1)/(12), v_(0) = 12 cm`
`m = (v_(0))/(u_(0))(1 + (d)/(f_(e))) = (12)/(6)(1 + (25)/(10)) = 7`
From `(1)/(v_(e)) - (1)/(u_(e)) = (1)/(f_(e))`
`(1)/(u_(e)) = (1)/(v_(e)) - (1)/(f_(e)) = (1)/(-25) - (1)/(10) = (-7)/(50)`
`u_(e) = - (50)/(7) = - 7.14 cm`
Length of compound microscope,
`l = v_(0) + |u_(e)| = 12 + 7.14 = 19.14 cm`
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