In a Young's double slit experiment $15$ fringes are observed on a small portion of the screen when light of wavelength $500 \mathrm{n}\mathrm{m}$ is used. Ten fringes are observed on the same section of the screen when another light source of wavelength $\lambda$ is used. Then the value of $\lambda$ is (in $\mathrm{n}\mathrm{m}$ ) __________.