Question

An object placed in front of a convex lens resulted in an image whose size is the same as the object. Find out the focal length of the convex lens, if the object distance is $30cm$.

• A. 15

Answer 1

The correct option is A 15
Given:
The object distance is $30cm$.
In a convex lens, the object is placed to the left of the optic centre, So, the object distance is negative, i.e. $u=-30cm$
Also, the size of the image is the same as that of the object. This happens only when the object is placed at the centre of curvature, as shown:


Since the image forms at the centre of curvature onto the right side of the optic centre $\text{O}$, the image distance, $v$ is positive and is equal to the object distance, i.e. $v=+30cm$
Using the lens equation, $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$,
$\frac{1}{f}=\frac{1}{30}-\left(\frac{1}{-30}\right)=\frac{1}{30}+\frac{1}{30}=\frac{2}{30}=\frac{1}{15}$
Since, the focus of a convex lens is onto the right side of the optic centre, focal length is positive.
$\therefore$ Focal length, $f=+15cm$