A concave shaving mirror has a radius of curv | vedclass

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(C) Given: Radius of curvature $R = 35.0 \, cm$. The focal length $f = R / 2 = 35.0 / 2 = 17.5 \, cm$. Since it is a concave mirror,$f = -17.5 \, cm$.

Vedclass · Accepted Answer

$10.5$

Vedclass · Answer

(C) Given: Radius of curvature $R = 35.0 \, cm$. The focal length $f = R / 2 = 35.0 / 2 = 17.5 \, cm$. Since it is a concave mirror,$f = -17.5 \, cm$.For an upright (virtual) image,the magnification $m = +2.5$.The magnification formula for a mirror is $m = -v / u$,so $v = -m \cdot u = -2.5 \cdot u$.Using the mirror formula: $1/f = 1/v + 1/u$.Substituting the values: $1 / (-17.5) = 1 / (-2.5 \cdot u) + 1 / u$.$1 / (-17.5) = (-1 + 2.5) / (2.5 \cdot u) = 1.5 / (2.5 \cdot u)$.$2.5 \cdot u = -17.5 \cdot 1.5$.$u = -(17.5 \cdot 1.5) / 2.5 = -7 \cdot 1.5 = -10.5 \, cm$.The distance of the mirror from the face is $|u| = 10.5 \, cm$.

$A$ concave shaving mirror has a radius of curvature of $35.0 \, cm$. It is positioned so that the upright image of a man's face is $2.5 \, \times$ the size of the face. How far is the mirror from the face in $cm$?

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