Answer
(a) $\frac{1}{25}s$
(b) $5.6$
Work Step by Step
(a) We know that the size of the aperture is directly proportional to the brightness of the light but the speed of the shutter is inversely proportional to the size of the aperture. As the brightness of the light is one-quarter, hence the shutter speed is given as $4(\frac{1}{100})=\frac{1}{25}s$.
(b) We know that
$\frac{A_f}{A_i}=\frac{\frac{1}{4}\pi D_f^2}{\frac{1}{4}\pi D_i^2}$
$\implies \frac{4A_i}{A_i}=\frac{(\frac{f}{f-number})^2}{(\frac{f}{11})^2}$
This simplifies to:
$\implies f_{number}=\sqrt{\frac{(11)^2}{4}}$
$\implies f_{number}=5.6$
