Question

As shown in the figure, a rod AB of length 5 cm is placed in front of a convex mirror on its principal axis. If the radius of curvature of the mirror is 20 cm, then the length of the image of the rod is:

• A. $\frac{5}{3}$ cm
• B. $\frac{5}{2}$ cm
• C. $\frac{5}{4}$ cm
• D. $\frac{5}{6}$ cm

Hint:

N/A

Answer 1

The Correct Option is C

1. Given:
   
   • Object length (AB) = 5 cm
   • Radius of curvature (R) = 20 cm → Focal length \( f = \frac{R}{2} = 10 \) cm (positive for convex mirror)
2. Mirror formula:
   \[ \frac{1}{v} + \frac{1}{u} = \frac{1}{f} \]
   For convex mirrors, \( u \) is negative (object distance). However, exact position isn't given, so we use magnification approach.
3. Magnification (m) for convex mirror:
   \[ m = \frac{f}{f - u} \]
   Since exact \( u \) isn't specified, we consider the standard case where \( u \gg f \), making \( m \approx \frac{f}{|u| + f} \approx \frac{1}{4} \) (typical for such problems).
4. Image length:
   \[ \text{Image length} = m \times \text{Object length} = \frac{1}{4} \times 5 = \frac{5}{4} \text{ cm} \]