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Question

A students plots a graph between inverse of magnification 1/m produced by a convex thin lens and the object distance $$u$$ as shown in figure. What was the focal length of the lens used?
617748_142422e64cc94b198b431d12556f6a49.png


A
bca
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B
bca
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C
cb
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D
bc
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Solution

The correct option is C $$\dfrac{c}{b}$$
Given,
Slope of the curve $$=\dfrac{b}{c}$$

Lens formula, $$\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}$$--------(1)

Multiply by $$u$$ in both side in equation (1)

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

$$\Rightarrow \dfrac{1}{m}-1=\dfrac{u}{f}$$

or $$\dfrac{1}{m}=(\dfrac{1}{f})u+1$$

this is the equation of a straight line whose slope

$$\dfrac{1}{f}=\dfrac{b}{c} $$

 $$ \therefore f=\dfrac{c}{b}$$

Physics

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