Question

a concave spherical mirror forms a 40 cm high realm image of an object whose height is 10 cm the radius of the mirror is 60 cm find the distance from the object to its image

Answer 1

hey bro here is ur answer...........
M=V/U=I/O=40/10=4
then
U=V/4
then
1/F=1/V-1/U
but F=R/2
then F=30cm
1/30=1/V+1/V/4
THEN
V=150cm
the U=V/4
THEN
U=27.5
THEN
U+V=177.5




HOPE HLP

Answer 2

${\bold{{\underline{\red{G}\pink{iv}\green{en}\purple{:-}}}}}$

• Height of image (h') = 40 cm
• Height of object (h) = 10 cm
• Radius of mirror (r) - 60 cm
• ∵ Focal length (f) = $\bold{\frac{r}{2}}$
• Focal length (f) = $\frac{-60}{2}$
• ∴ Focal length (f) = - 30 cm

${\bold{{\underline{\red{Formulas}\pink{\:to\:be}\green{\:used}\purple{:-}}}}}$

• Magnification (m) = $\bold{\frac{Image\:height\:(h')}{Object\:height\:(h)}}$                    

(or)

• Magnification (m) = $\bold{\frac{-\: Image\:distance\:(-v)}{Object\:distance\:(u)}}$

• $\bold{\frac{1}{Image\:distance\:(\frac{1}{v} )}\: +\: \frac{1}{Object\:distance\:(\frac{1}{u} )} \:=\:\frac{1}{Focal\:length\:(\frac{1}{f} )} }$

${\bold{{\underline{\red{Q}\pink{uest}\green{ion}\purple{:-}}}}}$

• To find the the distance of object from image (v + u) ?

${\bold{{\underline{\red{S}\pink{olut}\green{ion}\purple{:-}}}}}$

• Magnification (m) = $\bold{\frac{Image\:height\:(h')}{Object\:height\:(h)}}$

• Magnification (m)  =  $\bold{\frac{40}{10}}$

• Magnification (m) = 4 cm

• $\frac{-v}{u}$ = 4
• - v = 4u

        Also:

• Magnification (m) = $\bold{\frac{-\: Image\:distance\:(-v)}{Object\:distance\:(u)}}$

• $\bold{\frac{1}{Image\:distance\:(\frac{1}{v} )}\: +\: \frac{1}{Object\:distance\:(\frac{1}{u} )} \:=\:\frac{1}{Focal\:length\:(\frac{1}{f} )} }$

• $\bold{ \frac{1}{u} \: -\: {\frac{1}{4u}\:=\:\frac{1}{-30} }}$

• Lcm = - 4u

• $\frac{-4\:+\: 1}{-4u}\:=\:\frac{1}{-30}$

• $\frac{-3}{-4u}\:=\:\frac{1}{-30}$

• $\frac{1}{-4u}\:=\:\frac{1}{-30\:*\: -3}$

• 4u = - 90

• u = $\frac{-90}{4}$

• u = -22.50
• ∴ v = - 90

The the distance of object from image (v + u) = -(90 + 22.50)

• v + u = - 112.50

$\rule{200}{2}$