Question

the image formed by concave mirror is half of the object when the object is moved away from the mirror 30 cm , the size of the image becomes 1/3 of the object calculate radius of curvature ​

Answer 1

$\mathbb{QUESTION}$

$\text{the image formed by concave mirror is half of the object when the object }$ $\text{is}$$\text {moved away from the mirror 30 cm , the size of the image}$ $\text{becomes 1/3 of the object calculate radius of curvature ​}$

$\mathbb{SOLUTION}$

$\textsc{The mirror produces three times enlarged image.}$

$\text{So, magnification(m) = 3{}}$

$\textsc{WE KNOW, magnification of spherical mirrors = m = -v/u}$

$\text{Where v is the distance between image and mirror }$ $\text{and u is the distance between object and mirror.}$

$Here, u = -10 cm$

$=> 3 = -V/-10$

$=>v = 30$

$\textsf{So , the distance between image and mirror = 30 cm}$

$1/v + 1/u = 1/f(mirror formula)$

$1/30 + 1/-10 = 1/f$

$1/30 - 1/10 = 1/f$

$-2/30 = 1/f$

$-1/15 = 1/f$

$f = -15 cm$

$\textsf{We know radius of curvature}$ = $2f$

So, radius of curvature $= R = 2*-15 = -30 cm$ which is the required answer.

$\mathbb{SHORTCUT -}$

$\textsf{Remember the formula, }$$m = f/(f-u)$

$So, 3 = f/(f-(-10))$

$3 = f/(f+10)$

$\textsf{Cross multiply,}$

$3f + 30 = f$

$2f = -30$

$R = -30 cm \:\:\:(R= 2f).$

$\mathcal{HOPE\:IT\:HELPS\\}$

$\mathcal{BY\;BRAINLY\:ROSHAN}$