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Image Formation by Convex Lens

In the adjoin...

Question

In the adjoining ray-diagram are given the position of an object O, image I and two lenses $L_{1} a n d L_{2}$ . The focal length of $L_{1}$ is also given. Find the focal length of the lens $L_{2}$

30 cm

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-30 cm

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-15 cm

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None of these

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Solution

The correct option is C -15 cm
Using Lens maker formula,
$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}, f = + 15 c m$
u=-40 cm
(for first lens)
$\frac{1}{v} - \frac{1}{- 40} = \frac{1}{15}, v = + 24 c m$
This image acts as object for lens $L_{2}$
so, u = + (24-14) = +10 cm,
v=30cm
f=?
$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
$\frac{1}{f} = \frac{1}{+ 30} - \frac{1}{+ 10}$
f=-15 cm

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In the adjoining ray-diagram are given the position of an object O, image I and two lenses L1 and L2. The focal length of L1 is also given. Find the focal length of the lens L2

The correct option is C -15 cmUsing Lens maker formula, 1v−1u=1f,f=+15 cm u=-40 cm (for first lens) 1v−1−40=115,v=+24 cm This image acts as object for lens L2 so, u = + (24-14) = +10 cm, v=30cm f=? 1f=1v−1u 1f=1+30−1+10 f=-15 cm

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