Question

the image formed by a convex mirror of a focal length 30 cm is a quarter of the object.what is the distance of the object from the mirror

Answer 1

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Answer 2

The answer to the question is 90 cm i.e the object distance is 90 cm from the mirror.

CALCULATION:

As per the question, the focal length of the convex mirror f = 30 cm.

The magnification of the image m = $\frac{1}{4}$

We are asked to calculate the object distance [u].

As per the sign convention for reflection, the measurements taken along the direction of light is taken as positive and its reverse is taken as negative.

The transverse measurement above the principal axis is taken as positive and below the principal axis is taken as negative.

Hence, the focal length of the convex mirror f = +30 cm.

The image formed by a convex mirror is virtual and erect.

Hence, the magnification will be positive.

Hence, magnification m = $+\frac{1}{4}$ = +0.25

The relation between focal length, magnification and object distance is given as -

                                     $m=\ \frac{f}{f-u}$

                                     $u=\frac{m-1}{m}\times f$

                                     $=\frac{0.25-1}{0.25}\times -(30)$

                                     $=\ -90\ cm$        [ans]

    Here, the negative sign is due to the fact  that object distance is measured opposite to the direction of  light.