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A photographic plate records sufficiently intense lines when it is exposed for 12s to a source of 10W. How long should it be exposed to a 12W source radiating the light of same colour to get equally intense lines ?

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To get equally intense lines on the photographic plate, the radiant flux (energy) should be same.
So, 10W × 12sec = 12W × t
=> t =10Wx12 sec/12W= 10 sec.

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