Question

An object of height 1.5cm is placed at a distance of 45cm from the convex lens, the real image is formed at a distance of 30cm from the lens. Find the height of the image formed.

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Answer 1

✯ Given :-

• Convex Lens
• Height of the object = 1.5 cm
• Object Distance = -45 cm
• Image distance = 30 cm

✯ To find :-

• Height of the image formed.

✯ Solution :-

Here height of the image formed can be find by given formula -

${\large{ \underline{ \boxed{\bf{h'=-\frac{v \:h}{u} }}}}}$

Here

• h' = Height of the image
• v = Image distance
• u = Object distance
• h = Height of the object.

So, Height of the image formed is :-

${\sf{ \implies{h' = - \dfrac{vh}{u} }}}$

${\sf{ \implies{h' = - \cfrac{30 \times 1.5}{ - 45} }}}$

${\sf{ \implies{h' = - \cfrac{45}{ - 45} }}}$

${\sf{ \implies{h' =\cfrac{45}{ 45} }}}$

${ \large{ \underline{ \boxed{{\bf{ \implies{h' = 1 \: cm}}}}}}}$

So, Height of the image is 1 cm.

Answer 2

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Given:-

• $\bf h_{o}$ = 1.5cm
• $\bf u$ = -45cm
• $\bf v$ = 30cm ( in case of lenses the real image is +ve)

To find:-

• $\bf h_{i}$

Formula:-

$\longrightarrow$ ${\large{ \underline{ \boxed{\sf{h_{i}=\frac{ v}{u} × h_{o} }}}}}$

Solution:-

$\longrightarrow$ $\sf h_{i}$ = $\sf\dfrac{30}{-45}$ × $\sf 1.5$

$\longrightarrow$ $\sf h_{i}$ = $\sf\cancel\dfrac{45}{45}$

$\longrightarrow$ $\sf h_{i}$ = 1cm

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Additional information

• Cases in Concave mirror -
• it is same as Convex lens

$\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{cccc}\sf \pink{Position_{\:(object)}} &\sf \purple{Position_{\:(image)}} &\sf \red{Size_{\:(image)}} &\sf \blue{Nature_{\:(image)}}\\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\sf At \:Infinity &\sf At\: F&\sf Highly\:Diminished&\sf Real\:and\:Inverted\\\\\sf Beyond\:C &\sf Between\:F\:and\:C&\sf Diminished&\sf Real\:and\:Inverted\\\\\sf At\:C &\sf At\:C&\sf Same\:Size&\sf Real\:and\:Inverted\\\\\sf Between\:C\:and\:F&\sf Beyond\:C&\sf Enlarged&\sf Real\:and\;Inverted\\\\\sf At\:F&\sf At\:Infinity&\sf Highly\: Enlarged&\sf Real\:and\:Inverted\\\\\sf Between\:F\:and\:P&\sf \: Behind\:the\:mirror&\sf Enlarged&\sf \: Erect\:and\:Virtual\end{array}}\end{gathered}\end{gathered}\end{gathered}$

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hope it's beneficial ツ

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