Question

a convex mirror used for rear-raw on an automobile has a radius of curvature of 8m. If a bus is located at 10m from the mirror. Find the position,nature and size of the mirror...​

Answer 1

AnswEr :

Image formed is virtual, erect, and smaller in size by 0.44

Explanation :

We're given with a convex mirror which is used as rear-raw on an automobile with it's radius. Also, they've given that a bus is located at 10 m from the mirror.

So, here we're supposed to find out the position, nature and size of the mirror.

• Radius of curvature (R) = 8m

• Object distance (u) = - 10 m

We'll find the position, nature and size of the mirror in the sequence, that is, firstly focal length then image distance and at last magnification.

$\bigstar \: \: { \underline {\sf{Focal \: length \: is :}}}$

$:\implies \sf \: \:\dfrac{R}{2} \\ \\ \\ :\implies \sf \: \:\dfrac{8}{2} \\ \\ \\:\implies \sf \: \: \blue{+ 4 \: m.}$

Focal length will remain positive as radius of curvature is positive in the case of convex mirror.

By using mirror formula,

$:\implies \sf \: \: \dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f} \\ \\ \\:\implies \sf \: \:\dfrac{1}{v} = \dfrac{1}{f} - \dfrac{1}{u} \\ \\ \\ :\implies \sf \: \: \dfrac{1}{v} = \dfrac{1}{8} - \dfrac{1}{ - 10} \\ \\ \\ :\implies \sf \: \: \dfrac{1}{v} = \dfrac{-10-8}{ - 80} \\ \\ \\ :\implies \sf \: \: \dfrac{1}{v} = \dfrac{ - 18 }{ - 80} \\ \\ \\ :\implies \sf \: \:v = \dfrac{80}{18} \\ \\ \\ :\implies \sf \: \: \red{v = 4.4 \: m}$

$\bigstar \: \:{ \underline{ \sf{ Magnification :}}}$

$: \implies \sf \: \: \dfrac{h_{i}}{h} \\ \\ \\ : \implies \sf \: \: \dfrac{ - v}{u} \\ \\ \\ : \implies \sf \: \: \dfrac{ - 4.4}{ - 10} \\ \\ \\ : \implies \sf \: \: \green{+ 0.44}$

Therefore, Image formed is virtual, erect, and smaller in size by 0.44.