Question

The exposure time of a camera is 8ms for f- number 5.6. What will be the exposure time for f -number 8?
Option
a.2ms
b.16.32ms
c.8ms
d.4ms

Answer 1

Hint:The exposure time, or period of exposure, is usually understood to refer to the amount of time that a conventional camera's film or a modern digital camera's sensor is exposed to light in order to capture an image. In seconds, the exposure time is specified.
Formula used:
${\text{Time of exposure }}\alpha {\text{ (f}}{\text{. number }}{{\text{)}}^{\text{2}}}$

Complete answer:
Shutter speed, also known as exposure time, is the amount of time that the film or digital sensor within a camera is exposed to light, as well as the amount of time that the camera's shutter is open when taking a shot. The exposure duration is related to the amount of light that reaches the film or image sensor. One thousandth of a second lets in half as much light as one thousandth of a second. The f-number of an optical system, such as a camera lens, is the ratio of the focal length of the system to the diameter of the entry pupil in optics ("clear aperture"). It's also known as the focal ratio, f-ratio, or f-stop in photography, and it's highly significant. Stopping down refers to raising the f-number, which is a dimensionless number that is a quantitative measure of lens speed. The f-number is often represented by a lower-case hooked f in the pattern f/N, where N represents the f-number. The reciprocal of the relative aperture is the f-number (the aperture diameter divided by focal length).
${\text{Time of exposure }}\alpha {\text{ (f}}{\text{. number }}{{\text{)}}^{\text{2}}}$
Hence exposure time of a camera is 8ms for f- number 5.6
So,
$ \Rightarrow \dfrac{{{t_1}}}{{{f_1}^2}} = \dfrac{{{t_2}}}{{{f_2}^2}}$
Upon substituting the values we get
$\dfrac{8}{{{{5.6}^2}}} = \dfrac{{{t_2}}}{{{8^2}}}$
${t_{_2}} = \dfrac{{512}}{{31.36}}$
$ \Rightarrow {t_2} = 16.32ms$

Note:
Never forget to square the f number upon substituting. The physical aperture and focal length of the eye are used to calculate the f-number of the human eye. When the pupil is fully open, it may be as large as 6–7 mm in diameter, which corresponds to the maximum physical aperture.