First slide

The optical instruments

Question

A satisfactory photographic print is obtained when the exposure time is 10 sec at a distance of 2 m from a 60 cd lamp. The time of exposure required for the same quality print at a distance of 4 m from a 120 cd lamp is

Difficult

A

5 sec
B

10 sec
C

15 sec
D

20 sec

Solution

$I_{1} D_{1}^{2} t_{1} = I_{2} D_{2}^{2} t_{2} Here D is constant and I = \frac{L}{r^{2}} So \frac{L_{1}}{r_{1}^{2}} \times t_{1} = \frac{L_{2}}{r_{2}^{2}} \times t_{2} \Rightarrow \frac{60}{(2)^{2}} \times 10 = \frac{120}{(4)^{2}} \times t \Rightarrow 20 \sec$

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