The radius of curvature of a concave mirror i | vedclass

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(D) Given: Radius of curvature $R = -40 \ cm$ (for concave mirror),so focal length $f = R/2 = -20 \ cm$. Magnification $m = \pm 2$.Case $1$: For a rea

Vedclass · Accepted Answer

$30$

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(D) Given: Radius of curvature $R = -40 \ cm$ (for concave mirror),so focal length $f = R/2 = -20 \ cm$. Magnification $m = \pm 2$.Case $1$: For a real image,$m = -2$.Using the formula $m = f / (f - u)$:$-2 = -20 / (-20 - u)$$-2(-20 - u) = -20$$40 + 2u = -20$$2u = -60 \Rightarrow u = -30 \ cm$.Case $2$: For a virtual image,$m = +2$.Using the formula $m = f / (f - u)$:$2 = -20 / (-20 - u)$$2(-20 - u) = -20$$-40 - 2u = -20$$-2u = 20 \Rightarrow u = -10 \ cm$.Since $30 \ cm$ is the only option provided that matches the real image case,the correct answer is $30 \ cm$.

Column-$I$	Column-$II$
$1$. $m = -2$	a. Convex mirror
$2$. $m = -1/2$	b. Concave mirror
$3$. $m = +2$	c. Real image
$4$. $m = +1/2$	d. Virtual image

The radius of curvature of a concave mirror is $40 \ cm$ and the size of the image is twice that of the object. The object distance is $... \ cm$.

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Match the corresponding entries of Column-$I$ with Column-$II$. [Where $m$ is the magnification produced by the mirror]
Column-$I$ Column-$II$
$1$. $m = -2$ a. Convex mirror
$2$. $m = -1/2$ b. Concave mirror
$3$. $m = +2$ c. Real image
$4$. $m = +1/2$ d. Virtual image

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