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Question

# A camera takes a properly exposed photo at f /5.6 and 1/125 s. What shutter speed should be used if the lens is changed to f/4.0?

Solution

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$\textbf{Given values:}$

$f-number=5.6$

$\Delta t=\dfrac{1}{125} \: \text{s}$

We know $I \Delta t$ should be same:

\begin{align*} I&=\frac{1}{(f-number)^2}\\ \dfrac{\dfrac{1}{125}}{(5.6)^2}&=\frac{\Delta t}{(4)^2}\\ \Delta t&=\frac{16}{(5.6)^2} \times \frac{1}{125}\\ \Delta t&=\frac{0.510}{125}\\ \Delta t&=0.00408 \: \text{s}\\ \end{align*}

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