Question

An object is placed 40.0 cm in front of a convex mirror. The image appears 15 cm behind the mirror. What is the focal length of the mirror? 1 point + 24 c
m + 11 cm -24 cm - 11 cm

Answer 1

$\bold{\underline{\underline{ \bigstar\: Solution :}}}$

$\:\:$

$\footnotesize{ Distance\: between\: object\:and \: mirror = 40cm }$

$\footnotesize{\implies U = - 40cm }$

$\:\:$

$\rule{200}3$

$\:\:$

$\footnotesize{Image\:appears\: behind\: the\: mirror = 15cm}$

$\footnotesize{\implies V= 15cm}$

$\:\:$

$\rule{200}3$

$\:\:$

$\footnotesize{Focal\: length = \dfrac{1}{U} + \dfrac{1}{V} }$

$\footnotesize{\implies Focal\: length = \dfrac{1}{U} + \dfrac{1}{V} }$

$\footnotesize{\implies \dfrac{1}{F} = \dfrac{1}{U} + \dfrac{1}{V} }$

$\footnotesize{\implies \dfrac{1}{F} = \dfrac{1}{- 40cm} + \dfrac{1}{15cm} }$

$\footnotesize{\implies \dfrac{1}{F} = \dfrac{- 3 + 8}{120cm}}$

$\footnotesize{\implies \dfrac{1}{F} = \dfrac{5}{120cm}}$

$\footnotesize{\implies \dfrac{1}{F} = \dfrac{1}{24cm}}$

$\footnotesize{\implies F = 24cm }$

$\:\:$

$\bold{ \bigstar\: Focal\: length = 24cm}$

Answer 2

$\bf{\underline{\underline{ \bigstar\: Explanation : }}}$

$\:\:$

$\tt{\red{ \dfrac{1}{F} = \dfrac{1}{U} + \dfrac{1}{V}}}$

$\tt{\red{\implies \dfrac{1}{F} = \dfrac{1}{-40cm} + \dfrac{1}{15cm}}}$

$\tt{\red{\implies \dfrac{1}{F} = \dfrac{-3 + 8}{120cm} }}$

$\tt{\red{\implies \dfrac{1}{F} = \dfrac{5}{120cm} }}$

$\tt{\red{\implies \dfrac{1}{F} = \dfrac{1}{24cm} }}$

$\tt{\green{\implies 24cm = F }}$

$\:\:$

$\bold{ \bigstar\: Focal\: length : 24cm}$