Question

An object at a distance of 30 cm from a concave mirror gets its image at the same point. The focal length of the mirror is

• A. -30 cm
• B. 30 cm
• C. -15 cm
• D. 15 cm

Answer 1

The correct option is C

-15 cm

Step 1:

Given:

The object distance, $u=-30cm$

The image distance, $v=theobjectdis\tan ce=-30cm$

Step 2:

Finding the focal length of the concave mirror:

$$\begin{gathered} Weknowthat, \\ \frac{1}{u}+\frac{1}{v}=\frac{1}{f} \\ Bysubstitutingthegivenvalues,weget \\ \frac{1}{-30}+\frac{1}{-30}=\frac{1}{f} \\ \Rightarrow \frac{2}{-30}=\frac{1}{f} \\ \Rightarrow f=-15cm \end{gathered}$$

Hence, the correct option is option (C).