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Question

Lenses of powers $$3D$$ and $$-5D$$ are combined to from a composite lens. An object is placed at a distance of $$50\ cm$$ from this lens. Calculate the position of its image.


A
10 cm
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B
+10 cm
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C
25 cm
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D
+25 cm
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Solution

The correct option is C $$-25\ cm$$

Given,

Power $${{P}_{1}}=+3D\ \ and\ {{P}_{2}}=-5D$$

Position of object $$u=-50\,cm$$

Power gets added

 $$ P={{P}_{1}}+{{P}_{2}} $$

$$ P=3-5=-2 $$

$$ f=\dfrac{1}{P}=\dfrac{1}{-2}=-50\,cm $$

Apply lens formula

$$ \dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u} $$

$$ v=\dfrac{uf}{f+u}=\dfrac{\left( -50 \right)\times \left( -50 \right)}{\left( -50 \right)+\left( -50 \right)}=-25\,cm $$

Position of image is $$v=-25\,cm\ $$ 


Physics

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