I need help figuring out the following 3 formulas From measurements of the objec

Question

I need help figuring out the following 3 formulas

From measurements of the object distance o and image distance i one can calculate f, the focal length of a thin lens, using Equation = shows us that the relative uncertainty in the reciprocal of a quantity is the same as the relative uncertainty in the quantity itself. Enter a formula for the absolute uncertainty in 1/o in terms of o (use the substitution Deltao for the absolute uncertainty in o and beware: it's case - sensitive!). and, similarly, enter a formula for the absolute error in 1/i In terms of Ai (use the substitution Deltai for the absolute uncertainty in i and beware: it's case - sensitive!). Using Equation S enter a formu for the absolute uncertainty in (1/f) in terms of the substitutions Deltao Deltai . and i and beware: they are case - sensitive! Since the relative uncertainty in (1/f) and f are the same, i.e., you can find the absolute uncertainty in the focal distance f by multiplying the absolute uncertainty in [1/f) (from the last formula entered above) by f2 !

Explanation / Answer

we know that

relative uncertainty = absolute uncertainty / final measurement

absolute uncertainty = relative uncertainty * final measurement

we also know from above

delta(1/0) / (1/0) = delta(0) / 0

now coming to our problem

delta (1/0) = (delta (0) / 0 ) * (1/0)

1) delta(1/0) = delta(0) / 0^2

2) simillarly delta(1/i) = delta(i) / i^2

3) delta (1/f) =sqrt [(delta(0) / 0^2)^2 + (delta(i) / i^2)^2]

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