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

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#### Solution

For convex mirror, the focal length is always positive, f = +ve

An object is placed on the left side of the mirror. So, the object distance, u = −ve or u < 0. Using the mirror formula we have,

`1/"f" = 1/"v" + 1/"u"`

`1/"v" = 1/"f" - 1/"u"`

Since f > 0 and u < 0, then from the above equations, we get that v > 0 ⇒ v < 0

Hence, a virtual image is always formed at the backside of the mirror. Therefore, the image formed by the convex mirror is always virtual in nature, independent of the location of the object.

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