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Two lenses of power $3 D$ and $- 5 D$ are placed in contact to form a composite lens. An object is placed at a distance $50 cm$ from this composite lens. Find the position of the image.

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v = - 20 cm

v = - 25 cm

v = - 21 cm

None of these

answer is B.

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Detailed Solution

The position of image is

- 25 cm

.
Given data in the problem,
Power of lens 1,

P_{1} = 3 D

Power of lens 2,

P_{2} = - 5 D

Position of object

u = - 50 cm

So, the total power will be,

P = P_{1} + P_{2}

\Rightarrow P = 3 - 5

\Rightarrow P = - 2

And the focal length is,

f = \frac{1}{P}

\Rightarrow f = \frac{1}{- 2}

\Rightarrow f = - 50 cm

A negative sign indicates that the combined lens would be of diverging nature.
By using lens formula,

\frac{1}{v} - \frac{1}{u} = \frac{1}{f}

\Rightarrow \frac{1}{v} - \frac{1}{- 50} = \frac{1}{- 50}

\Rightarrow \frac{1}{v} + \frac{1}{50} = \frac{1}{- 50}

\Rightarrow \frac{1}{v} = \frac{- 1 - 1}{50}

\Rightarrow \frac{1}{v} = \frac{- 2}{50}

\Rightarrow v = - 25 cm

A negative sign indicates that the image will be formed on the same side as that of the object.

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