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