Question

An object is placed at a distance of $20\text{cm}$ from the pole of a concave mirror whose focal length is $20\text{cm}$. Then image is formed at

• A. $20\text{cm}$ from the pole of the mirror
• B. $40\text{cm}$ from the pole of the mirror
• C. at the pole of the mirror
• D. at infinity

Answer 1

The correct option is D

at infinity

Step 1: Given Data and Assumption:

1. The focal length of the concave mirror, $f=-20\text{cm}$
2. The distance of the object from the pole, $u=-20\text{cm}$
3. The signs are negative according to the sign convention.
4. Assume the distance of the image from the pole is .$v$

Step 2: Calculation:

The $u,v\text{and}f$ are related as follows:

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

Putting the values:

$$\begin{gathered} \frac{1}{v}+\frac{1}{-20}=\frac{1}{-20} \\ \frac{1}{v}=0 \\ v=\infty \end{gathered}$$

Thus, the image is formed at infinity.

Hence, the correct option (d).