I need to find the focal length of a lens by using equation 1/u + 1/v=1/f I have: u= 50+-3 mm v= 200+-5 mm I calculate the value of f as 40mm. Now i need to find the uncertainty in this value. I have two approaches, but only the second one is correct. I do not know what is wrong with the first one.
FIRST APPROACH : since f=(uv)/(u+v) Delta f/f= Fractional error of f= fractional error of u+ fractional error of v + fractional error of (u+v)
From this the uncertainty is 4.7 mm
SECOND APPROACH:we have Fractional error of 1/f = fractional error of f So delta( 1/f) = delta(f)/f^2 (*)
Similarly (*) is true for u and v in place of f
We have : delta(1/f) = delta(1/u) + delta(1/v)
So delta(f)/f^2= delta(u)/u^2 + delta(v)/v^2
From this delta(f) is 2.1mm which is correct
What is wrong with my first attempt?