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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(2f)

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(2f) 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 2f behind the lens.
Following the sign convention rules
Question ImageFor the image to be real and of the same size. By using the magnification formula for the lens,
⇒ m= +vu =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
⇒1=v-u
⇒ v=-u
Form the lens formula
1f=1v-1u
 Where
f = focal length of the lens u= distance of object from the lens
v= distance of the image formed
⇒ 1f=1-u-1u
⇒ 1f=-1-1u
⇒ 1f=-2u
⇒ u=-2f
So the object should be placed at a distance of twice the focal length of the convex lens.
Question Image 
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