Question

A 2.0 cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 10cm. the distance of the object from the lens is 15cm. Find the nature and position and size of the image . Also find its magnification​

Answer 1

$\huge{\underline{\underline{\red{\mathfrak{AnSwEr :}}}}}$

$\small{\underline{\blue{\sf{Given :}}}}$

• Object Height (h) = 2 cm
• Focal Length (f) = 10 cm
• Object Distance (u) = 15 cm
• Convex Lens

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$\small{\underline{\green{\sf{Solution :}}}}$

Lens Formula :

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

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Formula for Magnification is :

$\large \star {\boxed{\sf{m \: = \: \dfrac{v}{u} \: = \: \dfrac{h'}{h}}}}$

$\implies {\sf{\dfrac{30}{-15} \: = \: \dfrac{h'}{2}}}$

$\implies {\sf{-2 \: = \: \dfrac{h'}{2}}}$

$\implies {\sf{h' \: = \: -2 \: \times \: 2}}$

$\implies {\sf{h' \: = \: -4 \: cm}}$

• Height is -4 cm
• Nature is Real And Inverted
• Distance is 30 cm

Answer 2

Answer:

Here

Explanation: