Question

The image formed by a convex mirror of focal length 30 cm is a quarter of the size of the object. The distance of the object from the mirror is

Answer 1

Correct option is B. 90 cm
Given, focal length of a convex mirror, $$f=30cm$$, and $$\dfrac{n_i}{n_o}=\dfrac{1}{4}$$.

Where, $$n_i$$ and $$n_o$$ are the sizes of image and object.

Now, if $$u$$ and $$v$$ be the distances of object and image from the pole of the mirror,

Then, we know, $$-\dfrac{v}{u}=\dfrac{1}{4}$$, i.e., $$v=-\dfrac{u}{4}$$.

So, from the equation of mirror,

$$\dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}$$

$$\therefore \dfrac{1}{f}=-\dfrac{4}{u}+\dfrac{1}{u}$$

Or, $$\dfrac{1}{30}=-\dfrac{3}{u}$$

Or, $$u=-90$$

So, the distance of the object from the mirror is $$90cm$$.

Hence, the correct option is (B).