Question

Distance between an object and three times magnified real image is 40 cm. The focal length of the mirror used is ________ cm.

• A. \( -\dfrac{15}{2} \)
• B. \( -10 \)
• C. \( -20 \)
• D. \( -15 \)

Hint:

For real images formed by mirrors, magnification is always negative.

Answer 1

The Correct Option is D

Step 1: Use magnification formula for mirrors.
For mirrors, magnification is given by \[ m = \frac{v}{u} \] Given that the image is real and three times magnified, \[ m = -3 \]
Step 2: Express image distance in terms of object distance.
From \( m = \frac{v}{u} = -3 \), we get \[ v = -3u \]
Step 3: Use given distance between object and image.
The separation between object and image is \[ |v - u| = 40 \] Substituting \( v = -3u \), \[ |-3u - u| = 40 \Rightarrow 4|u| = 40 \Rightarrow u = -10 \text{ cm} \]
Step 4: Apply mirror formula.
Using \[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \] \[ \frac{1}{f} = \frac{1}{30} - \frac{1}{10} = -\frac{1}{15} \] \[ f = -15 \text{ cm} \]