Question

A real image magnified three times is formed when an object is placed 20 cm from a concave mirror. What is the focal length of the mirror?

• A. 20 cm
• B. 30 cm
• C. 15 cm
• D. 10 cm

Answer 1

The correct option is C 15 cm

Answer is C.
The lens equation expresses the quantitative relationship between the object distance ($d_o$), the image distance ($d_i$), and the focal length ($f$).

The equation is stated as follows:

$\frac{1}{f}=\frac{1}{d_i}+\frac{1}{d_o}$

The magnification equation relates the ratio of the image distance and object distance to the ratio of the image height ($h_i$) and object height ($h_o$).

The magnification equation is stated as follows:

$M=-\frac{d_i}{d_o}$

In this case, $d_o=20cm$ and $M=3$.

Therefore, $-d_i=M\times d_o=3\times 20=-60cm$

From this, $\frac{1}{f}=-\frac{1}{60}+\frac{1}{20}=15cm$.

Hence, the focal length f of the mirror is 15 cm.