In astronomy it is common to expose a photographic plate to a particular portion

Question

In astronomy it is common to expose a photographic plate to a particular portion of the night sky for quite some time in order to gather plenty of light. Before leaving a plate exposed to the night sky, Matt decides to test his technique by exposing two photographic plates in his lab to light coming through several pinholes. The source of light is 1.8 m from one photographic plate and the exposure time is 1.0 h. For how long should Matt expose a second plate located 4.8 m from the source if the second plate is to have equal exposure (that is, the same energy collected)?

Explanation / Answer

for equal exposure, since areas are same => energy gathered must be same since power decreases as inverse square of distance => P1T1 = P2T2 and P1/P2 = (R2/R1)^2 => T2 = (P1/P2)T1 = T1 x (R2/R1)^2 = 1 (4.8/1.8)^2 = 7 Hrs 6 min (approx.)

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