Question

A converging mirror with a radius of 20cm creates a real image at 30cm from the mirror what is the objects distance

Answer 1

$\large \underline{ \red{\underline{ \sf Question}}} : - \\ \sf A \: converging \: mirror \: with \: a \: radius \: of \: 20cm \\ \sf creates \: a \: real \: image \: at \: 30cm \: from \: the \: \\ \sf mirror \: what \: is \: the \: object \: distance \: .$

$\large \underline{ \green{\underline{ \sf \: Answer \: }}} : - \\ \sf object \: distance \: is \: 1 5 cm \:$

$\large \underline{ \red{\underline{ \sf To \: Find }}} \: - \\ \to \sf object \: distance \:$

$\large \underline{ \pink{\underline{ \sf Explanation }}} \: : -$

Given that :

• Image distance (v) = 30 cm

• Radius of curvature (R) = 20 cm

• Object distance (u) = ?

Note :-

→ Focal length of a converging mirror is positive .

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

we know that ,

$\to \sf \frac{2}{R} = \frac{1}{v} + \frac{1}{u} \\ \\ \rm putting \: the \: given \: values \: \\ \\ \to \sf \frac{2}{20} = \frac{1}{30} + \frac{1}{u} \\ \\ \to \sf \frac{1}{u} = \frac{1}{10} - \frac{1}{30} \\ \\ \to \sf \frac{1}{u} = \frac{3- 1}{30} \\ \\ \to \sf \frac{1}{u} = \frac{2}{30} \\ \\ \to \sf \frac{1}{u} = \frac{1}{15} \\ \\ \to \boxed{ \sf u = 15cm \: }$

•°• object distance is 15 cm

Answer 2

$\huge {\red{\boxed{ \overline{ \underline{ \mid\mathfrak{An}{\mathrm{sw}{ \sf{er}} \colon\mid}}}}}}$

Given :

• Mirror is concave
• Image Distance (v) = 30 cm
• Radius of Curvature (R) = 20 cm

Solution :

As we know that :

$\large \star {\boxed{\sf{R \: = \: 2f}}} \\ \\ \implies {\sf{2f \: = \: 20}} \\ \\ \implies {\sf{f \: = \: \dfrac{20}{2}}} \\ \\ \implies {\sf{f \: = \: 10 \: cm}}$

Focal length is 10 cm

_________________________________

Now use mirror formula :

$\large \star {\boxed{\sf{\dfrac{1}{f} \: = \: \dfrac{1}{v} \: + \: \dfrac{1}{u}}}} \\ \\ \implies {\sf{\dfrac{1}{u} \: = \: \dfrac{1}{f} \: - \: \dfrac{1}{v}}} \\ \\ \implies {\sf{\dfrac{1}{f} \: = \: \dfrac{1}{10} \: - \: \dfrac{1}{30}}} \\ \\ \implies {\sf{\dfrac{1}{u} \: = \: \dfrac{3 \: - \: 1}{30}}} \\ \\ \implies {\sf{\dfrac{1}{u} \: = \: \dfrac{2}{30}}} \\ \\ \implies {\sf{\dfrac{1}{u} \: = \: \dfrac{1}{15}}} \\ \\ \implies {\sf{u \: = \: 15 \: cm}}$

Object Position is 15 cm