Question

At what distance from a convex mirror of focal length $2.5\text{cm}$ should a small object be kept so that its image has a height of half of the original height of the object?

• A. $1\text{cm}$
• B. $2\text{cm}$
• C. $1.5\text{cm}$
• D. $2.5\text{cm}$

Answer 1

The correct option is D

$2.5\text{cm}$

The correct option is (D)

Step 1: Given data:

Focal length; f = 2.5 cm

Step 2: Formula used:

$m=\frac{heightofimage}{heightofobject}=-\frac{imagedis\tan ce}{objectdis\tan ce}$

Step 3: Calculation:

Let the actual height of the object be x cm

$m=\frac{{\displaystyle \frac{x}{2}}}{x}=\frac{1}{2}$

$$\begin{gathered} \frac{v}{u}=\frac{1}{2} \\ u=2v \end{gathered}$$

This means that the object must be placed at a distance twice the image distance

Object should be placed at the center of curvature = $2(2.5)=5cm$

Hence, the Object should be placed at center of curvature.