formula

Given: H, L Find: F

$Apply Pythagorean theorem: L^{2} + F^{2} = {(H + F)}^{2}$

$L^{2} + F^{2} = H^{2} + 2 H F + F^{2} | - F^{2}$

$L^{2} = H^{2} + 2 H F | - H^{2}$

$L^{2} - H^{2} = 2 H F | \div 2 H$

$\frac{L^{2} - H^{2}}{2 H} = F_{\min}$