Chapter 25, Problem 1P

To determine

The $f-\text{stop}$ required for a shutter speed of $\frac{1}{400}\text{s}$

Answer to Problem 1P

Solution:

The $f-\text{stop}$ required for a shutter speed of $\frac{1}{400}\text{s}$ is $f/8$.

Explanation of Solution

If exposure time is reduced by $1/8$, the area of the lens opening must increase by a factor of 4. Since area is proportional to square of the diameter, the diameter of the lens opening must be increased by a factor of 2.

But $f-\text{stop}=\frac{f}{D}$, if diameter of the opening of a lens increases by a factor of 2, the $f-\text{stop}$ of will reduce by a factor of 2. Hence new $f-\text{stop}$ will be $f/8$.