Question

A convex mirror of radius of curvature 4 meters is attached to a motor-bike to watch any other vehicle coming from behind. Calculate the location and position of the image of a vehicle which is 8 meters behind the bike at the time, as seen in the mirror.

Hint:

In convex mirrors, the image is always virtual, erect, and diminished regardless of the object position.

Answer 1

The radius of curvature \( R = 4 \, \text{m} \), so the focal length \( f = \frac{R}{2} = 2 \, \text{m} \).
The object distance \( u = -8 \, \text{m} \) (since the object is behind the mirror).
Using the mirror formula: \[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \] Substitute the values: \[ \frac{1}{2} = \frac{1}{v} - \frac{1}{8} \] Solving for \( v \) (image distance): \[ \frac{1}{v} = \frac{1}{2} + \frac{1}{8} = \frac{5}{8} \] \[ v = \frac{8}{5} = 1.6 \, \text{m} \] Thus, the image will be formed at a distance of \( 1.6 \, \text{m} \) behind the mirror (virtual image).