Question

The focal length of a convex lens is $30cm$and the size of the image is half of the object. The object distance is

• A. $30cm$
• B. $40cm$
• C. $60cm$
• D. $90cm$

Answer 1

The correct option is D

$90cm$

Step 1: Given Data-

The focal length of a convex lens is $30cm$

The size of the image is half of the object. That means, $m=-\frac{1}{2}$

We took the minus sign as per sign convention because all options are given greater than $30cm$, the focal length.

An object placed further than the focal length for a convex lens will give always an inverted real image.

Step 2: Establish a relationship between $u$and $v$-

We know that the magnification $m=\frac{v}{u}$

So we can write $m=-\frac{1}{2}=\frac{v}{u}$

Therefore, $-\frac{u}{2}=v$

Step 3: Calculate the object distance $u$-

We know the Lens equation $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

and putting $-\frac{u}{2}=v$ and $f=30cm$ into lens equation we get,

$\frac{1}{30}=-\frac{2}{u}-\frac{1}{u}$

$\Rightarrow u=-90 cm$.

Using sign convention, we conclude that the image should be placed $90 cm$away from the lens on left.

Hence, the correct option is (d) $90cm$.