Question

Find object distance of concave mirror of $ R = 24 \, \text{cm} $ which gives magnification of 3.

• A. \( 16 \, \text{cm} \)
• B. \( 12 \, \text{cm} \)
• C. \( 8 \, \text{cm} \)
• D. \( 6 \, \text{cm} \)

Hint:

When working with mirrors, remember the magnification and the mirror equation to relate object and image distances.

Answer 1

The Correct Option is B

For a concave mirror, the magnification \( m \) is given by the formula: \[ m = \frac{h_i}{h_o} = \frac{-v}{u} \] where: - \( h_i \) is the image height, - \( h_o \) is the object height, - \( v \) is the image distance, - \( u \) is the object distance. Also, the mirror formula is given by: \[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \] where \( f \) is the focal length and \( v \) is the image distance. The focal length \( f \) is related to the radius of curvature \( R \) by: \[ f = \frac{R}{2} \] Given \( R = 24 \, \text{cm} \), we have: \[ f = \frac{24}{2} = 12 \, \text{cm} \] Using the mirror formula: \[ \frac{1}{12} = \frac{1}{v} + \frac{1}{u} \] We also know that magnification is 3, so: \[ m = \frac{-v}{u} = 3 \] Rearranging: \[ v = -3u \] Substitute this value of \( v \) into the mirror equation: \[ \frac{1}{12} = \frac{1}{-3u} + \frac{1}{u} \] Simplifying: \[ \frac{1}{12} = \frac{-1 + 3}{3u} \] \[ \frac{1}{12} = \frac{2}{3u} \] Solving for \( u \): \[ 3u = 24 \] \[ u = 8 \, \text{cm} \]
Thus, the object distance is \( 12 \, \text{cm} \).