What is the nature of the lens and the position of the object if the image formed is of the same size as that of the object?

concave lens, at 2F₁

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convex lens, at 2F₁

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concave lens, at F₁

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convex lens, at F₁

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Solution

The correct option is C
convex lens, at 2F₁

From the ray diagram,

When the object is kept at ' $2 F_{1}$ ' (i.e., u = 2f), image formed will be real and inverted.

Object distance (u) = - 2f

Image distance (v) = 2f

Linear magnification (m) = $\frac{H e i g h t o f i m a g e}{H e i g h t o f o b j e c t} = \frac{v}{u}$

$\Rightarrow \frac{H_{i}}{H_{o}} = \frac{- 2 f}{2 f} = - 1$

$\Rightarrow H_{i} = - H_{o}$

Hence, height of the object is equal to the height of the image.

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