The distance between the object and the scree | vedclass

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(B) The displacement method formula for the focal length $f$ of a lens is given by $f = \frac{D^2 - x^2}{4D}$,where $D$ is the distance between the ob

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$5$

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(B) The displacement method formula for the focal length $f$ of a lens is given by $f = \frac{D^2 - x^2}{4D}$,where $D$ is the distance between the object and the screen,and $x$ is the distance between the two positions of the lens.Given $D = 100 \, cm$ and $x = 40 \, cm$.Substituting these values: $f = \frac{100^2 - 40^2}{4 	imes 100} = \frac{10000 - 1600}{400} = \frac{8400}{400} = 21 \, cm$.The power $P$ of the lens in Diopters $(D)$ is given by $P = \frac{100}{f(cm)}$.$P = \frac{100}{21} \approx 4.76 \, D$.Rounding to the nearest integer,we get $P \approx 5 \, D$.

The distance between the object and the screen is $100 \, cm$. $A$ lens produces an image on the screen when it is placed at either of two positions $40 \, cm$ apart. The power of the lens is (approximately): (in $, D$)

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