I am working on a calculator for you. It mimics the behavior of the Sample Size and Power calculators that are available through the JMP DOE menu. You can specify the sample size and compute the power. You can't go the other way yet. (It ain't fully cooked yet. If you try it, you break it.) It allows you to choose a two-sided test, lower one-sided test, or upper one-sided test. It assumes that you want a balanced or nearly balanced design. That is, if you enter 50 for a sample size, then it assumes that you will obtain a sample of 25 from each population.
By the way, the empirical power calculation available through the JMP Pro 13 Simulate feature that I mentioned in my previous reply and this exact closed form calculation agree very well. (But we don't always have a closed form to fall back on - love the new Simulate feature!)
Open and run the script. You must enter the alpha significance level of your test and the alternative hypothesis as the standard deviation for population 1 and 2. (Population 1 is the numerator of your F-test.) Then enter the candidate for your sample size and click Continue. Very fast way to evaluate the power with different sample sizes.