The distance between an object and a screen i | vedclass

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(D) Using the displacement method for a convex lens,the focal length $f$ is given by the formula:$f = \frac{D^2 - d^2}{4D}$where $D$ is the distance b

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$476$

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(D) Using the displacement method for a convex lens,the focal length $f$ is given by the formula:$f = \frac{D^2 - d^2}{4D}$where $D$ is the distance between the object and the screen,and $d$ is the distance between the two positions of the lens.Given $D = 100\, cm$ and $d = 40\, cm$.Substituting the values:$f = \frac{100^2 - 40^2}{4 	imes 100} = \frac{10000 - 1600}{400} = \frac{8400}{400} = 21\, cm$.The power of the lens $P$ in Diopters $(D)$ is given by $P = \frac{100}{f(cm)}$:$P = \frac{100}{21} D$.We are given $P = \left(\frac{N}{100}ight) D$,so:$\frac{N}{100} = \frac{100}{21} \approx 4.7619$.$N = \frac{10000}{21} \approx 476.19$.Rounding to the nearest integer,$N = 476$.

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