The image distance is ____ to the object distance in a plain mirror.

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Detailed Solution

The image distance in a plain mirror is the same as the object distance.
The focus of the plain mirror is infinite, and the image formed by a plain mirror is laterally inverted. Using the mirror formula

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

Where

f

u

and

v

are the focal length, object distance and image distance respectively.
We know that the focus of the plain mirror is infinite, therefore

\Rightarrow \frac{1}{\infty} = \frac{1}{v} + \frac{1}{(- u)}

\Rightarrow 0 = \frac{1}{v} - \frac{1}{u}

\Rightarrow \frac{1}{u} = \frac{1}{v}

\Rightarrow v = u

The image distance is the same as the object distance.

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