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?

A
bca
B
bca
C
cb
D
bc

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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