Question

An object of size 3cm is placed in front of a spherical mirror. A real, inverted image of size 3 cm is obtained on a screen which is placed at 20cm from the mirror. Find focal length of the mirror.​

Answer 1

$\large{\underline{\underline{ \bf{⎆Question:-}}}}$

• An object of size 3cm is placed in front of a spherical mirror. A real, inverted image of size 3 cm is obtained on a screen which is placed at 20cm from the mirror. Find focal length of the mirror.

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$\large{\underline{\underline{ \bf{♂Solution:-}}}}$

$\underline{ \boxed{ \sf{➥Gìven }}}$

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• Object size (h) : 3 cm
• Image size (h') : 3 cm
• Image distance (v) : 20 cm
• The mirror is spherical .
• Image is real .
• Image is inverted .

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$\underline{ \boxed{ \sf{➥Let }}}$

• Object distance = u

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$\small{\underline{\underline{ \bf{ᗒTo \: find :-}}}}$

• Focal length (L) of the mirror

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$\huge\underline{\overline{\mid{\bold{\bold{⤞Here}}\mid}}}$

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$\small{\underline{\underline{ \bf{⤞Mirror \: Formula :-}}}}$

$\underline{ \boxed{ \sf{ ✰ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} }}}$

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$\small{\underline{\underline{ \bf{ ●Magnification :-}}}}$

$\underline{ \boxed{ \sf{ ✰ \frac{h'}{h} = \frac{- v}{ \: \: \: \: u} }}}$

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Putting the values of h' , h and v :

$\longmapsto \frac{3}{3} \: = \: \frac{ - 20}{ \: \: \: \: \: u}$

$\longmapsto u\: = \: + 20 ( Sign \: \: convention )$

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Putting the values of v and u in mirror formula :

$\longmapsto \frac{1}{f} = \frac{1}{v} + \frac{1}{u}$

$\longmapsto \frac{1}{f} = \frac{1}{20} + \frac{ \: \: 1}{ 20}$

$\longmapsto \frac{1}{f} = \frac{1 + 1}{20}$

$\longmapsto \frac{1}{f} = \frac{2}{20}$

$\longmapsto \frac{1}{f} = \frac{1}{10}$

$\longmapsto f \: = \: 10 \: cm$

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• Hence the focal length is 10 cm .