Question

A camera takes a properly exposed photo with a $3\mathrm{mm}$diameter aperture and a shutter speed of $1/125\mathrm{s}.$. What is the appropriate aperture diameter for a $1/1500\mathrm{s}$shutter speed?

Short answer

The Diameter of the aperture is$6\sqrt{3}\mathrm{mm}$.

Step-by-step solution

Given information

We have given,

Diameter of the aperture = $3\mathrm{mm}$

Shutter speed = $\frac{1}{125}s$

We have to find the diameter of the aperture at shutter speed$1/1500\mathrm{s}.$

Simplify

We know that

$$\begin{gathered} \mathrm{I}\propto {\mathrm{D}}^2 \\ {\mathrm{I}}_1△{\mathrm{t}}_1={\mathrm{I}}_2△{\mathrm{t}}_2 \end{gathered}$$

Then,

$$\begin{gathered} \frac{{\mathrm{D}}_2^2}{{\mathrm{D}}_1^2}=\frac{△t_1}{△t_2} \\ {D}_2^2=\frac{1500}{125}\times 9=108 \\ {D}_2=6\sqrt{3}mm. \end{gathered}$$