Question
A compound microscope is used to enlarge an object kept at a distance 0.03m from it’s objective which consists of several convex lenses in contact and has focal length 0.02m. If a lens of focal length 0.1m is removed from the objective, then by what distance the eye-piece of the microscope must be moved to refocus the image
Answer: Option D
:
D
If initially the objective (focal length F0) forms the image at distance v0then v0=u0f0u0−f0=3×23−2=6cm
Now as in case of lenses in contact 1F0=1f1+1f2+1f3+.....=1f1+1F′0{where1F′0=1f2+1f3+...}
So if one of the lens is removed, the focal length of the remaining lens system
1F′0=1F0−1f1=12−110⇒F′0=2.5cm
This lens will form the image of same object at a distance v′0such that v′0=u0F′0u0−F′0=3×2.5(3−2.5)=15cm
So to refocus the image, eye-piece must be moved by the same distance through which the image formed by the objective has shifted i.e. 15 – 6 = 9 cm.
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:
D
If initially the objective (focal length F0) forms the image at distance v0then v0=u0f0u0−f0=3×23−2=6cm
Now as in case of lenses in contact 1F0=1f1+1f2+1f3+.....=1f1+1F′0{where1F′0=1f2+1f3+...}
So if one of the lens is removed, the focal length of the remaining lens system
1F′0=1F0−1f1=12−110⇒F′0=2.5cm
This lens will form the image of same object at a distance v′0such that v′0=u0F′0u0−F′0=3×2.5(3−2.5)=15cm
So to refocus the image, eye-piece must be moved by the same distance through which the image formed by the objective has shifted i.e. 15 – 6 = 9 cm.
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