A convex mirror always produces a virtual image independent of the location of the object. Use mirror equation to prove it.

Solution

Using mirror formula,

\frac{1}{v} + \frac{1}{u} = \frac{1}{f}

\Rightarrow

\frac{1}{v} = \frac{1}{f} - \frac{1}{u}

Object distance u is negative and the focal length f is positivefor convex mirror.

Therefore,

\frac{1}{v} = \frac{1}{+ f} - \frac{1}{- u} = \frac{1}{f} + \frac{1}{u}

which, is a positive quantity.

This implies, the image distance is always positive in case of convex mirror and the image is always formed on the other side of the object i.e., behind the convex mirror. Hence, the convex mirror always form a virtual image.

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Wave Optics

A convex mirror always produces a virtual image independent of the location of the object. Use mirror equation to prove it.

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