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Is it true that when an object is placed at $2 F$ of a convex lens, an image formed will be of the same size as that of the object?

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True

False

answer is A.

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Detailed Solution

The above statement is true.
When the object is placed at

2 F

, the image will be formed at the

2 F

on the other side of the lens, and it will be of the same size as that of the object.
Question Image

Let us say an object is placed at

2 F

from the optical centre. Let us find the image using the
lens formula for a convex lens-
⇒

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

where

f

is the focal length

v

is the image distance and

u

is the object distance.
Now let us place the object at

u = - 2 f

(the centre of curvature). The negative sign indicates that the distance measured from the optical centre is opposite to the direction of the ray of light. Using the lens formula-
⇒

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

⇒

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

⇒

\frac{1}{v} = \frac{1}{2 f}

\Rightarrow

v = 2 f

So, when the object is placed at the centre of curvature, the image distance is equal to object distance and there is no magnification of the image.

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