Question

The image formed by the convex mirror is \( \frac{1}{n} \) times the object and has a focal length \( f \). What is the distance of the object from the mirror?

• A. \( (n + 1)f \)
• B. \( (n - 1)f \)
• C. \( \left( \frac{n + 1}{n} \right) f \)
• D. \( \left( \frac{n - 1}{n} \right) f \)

Hint:

In convex mirrors, use magnification \( m = \frac{v}{u} \), and apply the mirror formula carefully.

Answer 1

The Correct Option is C

For a convex mirror: Magnification \( m = \frac{v}{u} = \frac{1}{n} \) (negative for virtual image, but here we use magnitude) So, \[ v = \frac{u}{n} \] Using the mirror formula: \[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} = \frac{n}{u} + \frac{1}{u} = \frac{n + 1}{u} \] \[ \Rightarrow u = \frac{n + 1}{f} \Rightarrow \text{Object distance} = \left( \frac{n + 1}{n} \right) f \]