Question

A camera takes a properly exposed photo at $\mathrm{f}/5.6$and $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$125$}\right.s$. What shutter speed should be used if the lens is changed to $\mathrm{f}/4.0$?

Short answer

The shutter speed is$\frac{1}{245}s.$

Step-by-step solution

Given information 

We have given,

$$\begin{gathered} \mathrm{f}-\mathrm{number}=5.6 \\ \mathrm{Shutter}\mathrm{speed}=\frac{1}{125} \end{gathered}$$

we have to find the shutter speed at$\mathrm{f}-\mathrm{number}=4.$

Simplify

The light intensity on the detector is related to the lens’s f-number by

$\mathrm{I}\propto \frac{{\mathrm{D}}^2}{{\mathrm{f}}^2}=\frac{1}{{(\mathrm{f}-\mathrm{number})}^2}$

from this formula we can say that

$$\begin{gathered} {\mathrm{I}}_1=\frac{1}{{(5.6)}^2} \\ {\mathrm{I}}_2=\frac{1}{{\left(4\right)}^2} \end{gathered}$$

and,

$$\begin{gathered} {\mathrm{I}}_1△{\mathrm{t}}_1={\mathrm{I}}_2△{\mathrm{t}}_2 \\ △{\mathrm{t}}_2=\frac{16}{{(5.6)}^2}\times \frac{1}{125}=\frac{1}{245}\mathrm{s} \end{gathered}$$