Sun rays are focussed on a photo-sensitive plate with the help of convex lens. The photo-electric current is found to be i. If the lens is replaced by another similar lens of half the diameter and double the focal-length, the photo-current will now be

A
i / 2
B
i /4
C
i / 8
D
i / 16

Solution:

we know that $i \propto D^{2} / f^{2}$
$\frac{i_{1}}{i_{2}} = {(\frac{D_{1}}{D_{2}})}^{2} \times (\frac{f_{2}}{f_{1}}) = (2)^{2} \times (2)^{2} or i_{2} = i_{1} / 16$

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