Question

If the distance between object and its two times magnified virtual image produced by a curved mirror is 15 cm, the focal length of the mirror must be :

• A. 15 cm
• B. -12 cm
• C. -10 cm
• D. 10/3 cm

Answer 1

Answer: (C)

-10 cm

Answer 2

Given:
- Magnification, $m = +2$ (since the image is virtual and magnified).
- Distance between the object and the image, $|u - v| = 15 \, \text{cm}$.

For a mirror, the magnification $m$ is given by:

$m = -\frac{v}{u}$

Since $m = +2$:

$-\frac{v}{u} = 2 \implies v = -2u$

Step 1. Set up the distance equation:

$|u - v| = 15$

Substitute $v = -2u$:

$|u - (-2u)| = 15$

$|3u| = 15$

$u = 5 \, \text{cm}$

Step 2. Calculate $v$:

$v = -2u = -2 \times 5 = -10 \, \text{cm}$

Step 3. Use the mirror formula:
The mirror formula is: $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$

Substitute $u = 5 \, \text{cm}$ and $v = -10 \, \text{cm}$:

$\frac{1}{f} = \frac{1}{-10} + \frac{1}{5} = -\frac{1}{10} + \frac{2}{10} = \frac{1}{10}$

$f = 10 \, \text{cm}$

Thus, the focal length of the mirror is $-10 \, \text{cm}$.

The Correct Answer is : -10 cm