Question

The distance between an object and a screen is $100 \,cm$ A lens can produce real image of the object on the screen for two different positions between the screen and the object. The distance between these two positions is $40\, cm$ If the power of the lens is close to $\left(\frac{ N }{100}\right) D$ where $N$ is an integer, the value of $N$ is ______.

Answer 1

Using displacement method
$f =\frac{ D ^{2}- d ^{2}}{4 D }$
Here, $D=100 \,cm$
$ d =40 \,cm$
$f =\frac{100^{2}-40^{2}}{4(100)}=21 \,cm$
$P =\frac{1}{ f }=\frac{100}{21} D $
$\frac{ N }{100}=\frac{100}{21} $
$N =476$