With diaphragm of the camera lens set at `(f)/(2)` , the correct exposure time is `(1)/(100)` , then with diaphragm set at `(f)/(4)`. Calculate the correct exposure time.

Explanation

As exposure time `prop(1)/(("aperture")^(2)) implies t_(1) prop (1)/([f//2]^(2)) "and" t_(2) prop (1)/([f//4]^(2))`
here `t_(1) = (1)/(100)"s then" (t_(2))/(t_(1)) = (16)/(4) = 4 implies t_(2) = 4t_(1) = (4)/(100)"s"`