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प्रश्न
Answer the following question in detail.
Derive the expressions for the magnifying power and the length of a compound microscope using two convex lenses.
उत्तर
- The final image formed in compound microscope (A′′ B′′) as shown in the figure, makes a visual angle β at the eye.
- The visual angle made by the object from distance D is α.
Compound Microscope - From figure,
tan β = `("A"”"B"”)/"v"_"e"=("A"’"B"’)/"u"_"e"`
and tan α = `"AB"/"D"` - Angular magnification or magnifying power of a compound microscope is given by,
M = `β/α≈(tan(β))/tan(α)`
= `"A’B’"/"u"_"e"xx"D"/"AB"=("A’B’")/"AB"xx"D"/"u"_"e"`
Where, `(("A’B’")/"AB")="v"_"o"/"u"_"o"` = mo is the linear (lateral) magnification of objective and `(("D")/"u"_"e")` = Me is the angular magnification or magnifying power of the eye lens.
∴ M = mo × Me - The length of the compound microscope is the distance between the two lenses, L = vo + ue.
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