Question

When a photograph is taken, the exposure time, t is directly proportional to the square of the size, f , of the opening in the camera lens. t = 0.02 when f = 8. It can be shown that t = 1/3200 f squared. Calculate the value of f when t = 0.0098

Answer 1

f = 5.6

Explanation:

given the quantities are proportional then the equation relating them is

t = kf² ← k is the constant of proportionality

To find k use the condition t = 0.02 when f = 8

k =
`(t)/(f^(2) )` =
`(0.02)/(64)` =
`(1)/(3200)`

t =
`(f^(2) )/(3200)` ← equation of proportionality

when t = 0.0098, then

0.0098 =
`(f^(2) )/(3200)` ( multiply both sides by 3200 )

f² = 0.0098 × 3200 ( take the square root of both sides )

f =
`√(0.0098(3200))` = 5.6