In a laboratory four convex lenses $L_{1}, L_{2}, L_{3}$ and $L_{4}$ of focal lengths $2, 4, 6$ and $8$ cm respectively are available. Two of these lenses form a telescope of length $10$ cm and magnifying power $4$ . The objective and eye lenses are respectively :

L_{2}, L_{3}

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L_{1}, L_{4}

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L_{1}, L_{2}

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L_{4}, L_{1}

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Solution

The correct option is D $L_{4}, L_{1}$
Let the focal length of the objective lens and eye piece be $f_{o}$ and $f_{e}$ respectively.
Magnifying power of telescope, $M = \frac{f_{o}}{f_{e}}$
$∴$ $4 = \frac{f_{o}}{f_{e}}$ $⟹ f_{o} = 4 f_{e}$ ..........(1)

Length of the telescope, $L = f_{o} + f_{e}$

$\Rightarrow$ $10 = f_{o} + f_{e}$

$\Rightarrow 10 = 4 f_{e} + f_{e}$ ......... using (1)

$\Rightarrow 10 = 5 f_{e}$ $⟹ f_{e} = 2$ cm

$\Rightarrow$ $f_{o} = 4 \times 2 = 8$ cm

Thus, the objective lens and eye lens must be $L_{4}$ and $L_{1}$ respectively.

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In a laboratory four convex lenses L1,L2,L3 and L4 of focal lengths 2,4,6 and 8cm respectively are available. Two of these lenses form a telescope of length 10cm and magnifying power 4. The objective and eye lenses are respectively :

In a laboratory four convex lenses $L_{1}, L_{2}, L_{3}$ and $L_{4}$ of focal lengths $2, 4, 6$ and $8$ cm respectively are available. Two of these lenses form a telescope of length $10$ cm and magnifying power $4$ . The objective and eye lenses are respectively :