Question

Draw a ray diagram for the formation of the image of an object by a convex mirror. Hence, obtain the mirror equation.

Hint:

A convex mirror always forms a virtual, erect, and diminished image, making it ideal for rearview mirrors.

Answer 1

Image Formation by a Convex Mirror 
- A convex mirror always forms a virtual, erect, and diminished image behind the mirror.
- The image is always located between the pole and focus of the mirror. 


Derivation of the Mirror Equation
Using the sign convention:
- The mirror formula is given by: \[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \] where:
- \( f \) = Focal length of the mirror
- \( u \) = Object distance
- \( v \) = Image distance
For a convex mirror, \( f \) and \( v \) are positive, while \( u \) is negative. Thus, the mirror equation holds for both concave and convex mirrors.