An object is placed in front of a convex mirr | vedclass

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(A) As shown in the figure,the plane mirror forms an erect and virtual image of the same size at a distance of $30\, cm$ behind it. Since the distance

Vedclass · Accepted Answer

$\frac{1}{5}$

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(A) As shown in the figure,the plane mirror forms an erect and virtual image of the same size at a distance of $30\, cm$ behind it. Since the distance between the object and the plane mirror is $30\, cm$,the image formed by the plane mirror is at a distance of $30\, cm$ behind the plane mirror. The distance of the plane mirror from the convex mirror is $50\, cm - 30\, cm = 20\, cm$. Let $P$ be the pole of the convex mirror and $M$ be the position of the plane mirror. The image $I$ formed by the plane mirror is at a distance of $30\, cm$ behind $M$. The distance of this image $I$ from the pole $P$ of the convex mirror is $PI = MI - MP = 30\, cm - 20\, cm = 10\, cm$. Since there is no parallax,the image formed by the convex mirror also forms at this position. For the convex mirror,the object distance $u = -50\, cm$ and the image distance $v = +10\, cm$. The magnification $m$ is given by $m = -\frac{v}{u} = -\frac{10}{-50} = \frac{1}{5}$.

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