Question

An object is placed in front of a convex mirror at a distance equal to the focal length of the mirror. If its focal length is $20cm$ , the distance of the image from the mirror is ……cm.

• A. $10$
• B. $20$
• C. $40$
• D. infinity

Answer 1

The correct option is A

$10$

Step 1: Given data:

An object is placed in front of a convex mirror at a distance equal to the focal length of the mirror. If its focal length is $20cm$ , the distance of the image from the mirror is $10$ cm.

Given ,

$f=20cm$ and as object is placed at the same distance as that of focus $\Rightarrow u=-20cm$ (negative sign implies that the object is on the left side of the lens)

We need to find the position of the image$\left(v\right)$.

Step 2: Finding the image distance:

Using the mirror formula , $\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$

$$\begin{gathered} \Rightarrow \frac{1}{20}=\frac{1}{-20}+\frac{1}{v} \\ \Rightarrow \frac{1}{v}=\frac{1}{20}+\frac{1}{20}=\frac{2}{20}=\frac{1}{10} \\ \Rightarrow v=10cm \end{gathered}$$

Thus, the correct option is (a).