Question

An object of 5 cm is placed 20
in front of a convex mirror of
radius30 cm Find the location, magnification and height of the image​

Answer 1

$\large\underline{\bigstar \: \: {\sf Given-}}$

In Convex Lens -

• Object is at (u) = - 20cm
• Radius of Curvature (R) = 30cm
• Height of object ${\sf h_o}$ = 5cm

Object Distance is negative Because it is at left side of mirror.

$\large\underline{\bigstar \: \: {\sf To \: Find -}}$

• Location of Image
• Magnification or image
• Height of image

$\large\underline{\bigstar \: \: {\sf Formula \: Used -}}$

$\implies\underline{\boxed{\sf \dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}}}$

$\implies\underline{\boxed{\sf Magnification \: (m)=\dfrac{-v}{u}}}$

$\implies\underline{\boxed{\sf m=\dfrac{h_i}{h_o}}}$

$\large\underline{\bigstar \: \: {\sf Solution-}}$

$\implies{\sf \dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}}$

We know that -

$\implies{\bf R=2f}$

$\implies{\sf 30=2f}$

$\implies{\sf f=\dfrac{30}{2}}$

$\implies{\sf f=15cm }$

$\bullet\underline{\bf Location \; of \: image -}$

$\implies{\sf \dfrac{1}{15}=\dfrac{1}{v}+\left(-\dfrac{1}{20}\right)}$

$\implies{\sf \dfrac{1}{15}=\dfrac{1}{v}-\dfrac{1}{20} }$

$\implies{\sf \dfrac{1}{v}=\dfrac{1}{15}+\dfrac{1}{20}}$

$\implies{\sf \dfrac{1}{v}=\dfrac{5+20}{20×5}}$

$\implies{\sf \dfrac{1}{v}=\dfrac{25}{100} }$

$\implies{\sf v=\dfrac{100}{25} }$

$\implies{\bf v=4\:cm}$

$\bullet$ Any position of object in a Convex mirror image is formed always between Pole (P) and Focus (F)

$\bullet$ Behind the Mirror

$\bullet$ Small, erect & virtual

$\bullet\underline{\bf Magnification \: of \; image -}$

$\implies\underline{\boxed{\sf m=\dfrac{-v}{u}}}$

$\implies{\sf m=\dfrac{-4}{5} }$

$\implies{\bf m=-0.8}$

Magnification of image is -0.8

$\bullet\underline{\sf Height \; of \; image -}$

$\implies\underline{\boxed{\sf m=\dfrac{h_i}{h_o}} }$

${\sf h_i= Height \; of \: image }$

${\sf h_o=Height \; of \: object}$

$\implies{\sf 0.8=\dfrac{h_i}{5} }$

$\implies{\sf h_i=5×0.8 }$

$\implies{\bf h_i=4\:cm }$

Height of image is 4cm