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Wave Optics

Question

Use the mirror equation to deduce that:
a convex mirror always produces a virtual image independent of the location of the object.

Solution

For convex mirror, f > 0 and for an object of left, u < 0.
From mirror formula,

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

\Rightarrow

\frac{1}{v} > 0 or v > 0

This shows that whatever be the value of u, a convex mirror form a virtual image on the right (because v is positive).