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Q.

Where should an object be placed in front of a convex lens to get a real image of the same size as the object?

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a

At the principal focus of the lens(

f

)

b

At infinity

c

At twice the focal length(

2 f

)

d

Between the optical centre of the lens and its principal focus.

answer is C.

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Detailed Solution

The object should be placed at a distance of twice the focal length in front of a convex lens to get a real and same-size image of the object.
When an object is placed at a distance of twice the focal length(

2 f

) in front of a convex lens, then the image will be formed of the same size as that of the object, real and inverted. The image will be formed at a distance of

2 f

behind the lens.
Following the sign convention rules

Question Image

For the image to be real and of the same size. By using the magnification formula for the lens,

\Rightarrow

m = + \frac{v}{u} = 1

(since the image is of equal size as that of the object )
Where

m = magnification of the lens

u = distnace of object from the lens

v = distance of the image formed

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

\Rightarrow v = - u

Form the lens formula

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

Where

f = focal length of the lens

u = distance of object from the lens

v = distance of the image formed

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

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

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

\Rightarrow u = - 2 f

So the object should be placed at a distance of twice the focal length of the convex lens.
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