Optics question

[math4me]

I am trying to find F, i have L = 60cm and U = 31cm, how would i calculate f (focal length)???

and also how would i find the uncertainties?

thank you very much

[Kurdt]

Not sure about the uncertainties but I assume U and L are object and image distances so the formula you need is

\frac{1}{L} + \frac{1}{U} = \frac{1}{F}

[mmwave]

I don't what else you were given to work with but the general rule for calculating uncertainties is

|df/dx| * Uncert. in x + |df/dy| * Uncert. in y

In your case, x could be L and y could be U. The derivatives would be partial deriv. of course. If you're not familar with partial derivatives then you can do it the hard way. Make both L & U smaller by their uncertainties and calc. f. Then make them both larger by the same amounts and recalc. f. The differences between these two f values and the one calc. with the given U & L values would be the uncertainties.

If you are not given the uncertanties in U & L then you have to estimate them. If they are measured, you can estimate the uncertainty as 1/2 of the smallest division on the ruler. If not, you can use the significant figures in their values as a guesstimate. 30 cm +/- 1 cm for example.