Question

a particular camera has a focal length of 35 millimeters (mm). a photographer wants to get a closeup of geological formation just about one and a third foot away or at a value of 0.4 meter. a standard equation applies as follows to find image distance (i) involving object distance (o) and focal length (f).
\\(\frac{1}{i}=\frac{1}{f}-\frac{1}{o}\\)
since the focal lengths are expressed in mm, all values will be included in the formula in mm.
\\(\frac{1}{i}=\frac{1}{35}-\frac{1}{400}\\)
what is the lowest value that can be used for the denominator to complete the equation?

Explanation:

Step1: Find the least - common multiple (LCM)

We need to find the LCM of 35 and 400 to complete the subtraction of the fractions $\frac{1}{35}-\frac{1}{400}$.

Step2: Prime - factorize the numbers

Prime - factorize 35 = 5×7 and 400 = 2×2×2×2×5×5.

Step3: Calculate the LCM

The LCM is 2×2×2×2×5×5×7 = 2800.

Answer:

2800