If the correct exposure of a certain scene is 130s at f11 wh

If the correct exposure of a certain scene is 1/30s at f/11, what is the correct exposure at f/2.0? t=______ms

Solution

The energy deposited in the detector is proportional to the intensity and exposure time

E = I t

for the two lenses must leave the same energy in the detector, so

I1 t1 = I2 t2

also the intensity is related to the number f

I = (1/#f)²

(1/#f1)² t1 = (1/#f2)² t2

Calculate

t2 = (#f2/#f1)² t1

t2 = (2/11)^2 *1/30

t2 = 0.001101 s = 1.11 ms