The kinetic energy’s of photo electrons emitted from metal are $K_1$ and  $K_2$ when irradiated with radiations of wave length ${\lambda }_1$ and  ${\lambda }_2$ respectively. The work function of the metal is

We know by photoelectric equation

$\mathrm{h\upsilon }=\mathrm{K}+\mathrm{\psi }$

where $\mathrm{h\upsilon }$ is the energy of the photon, $\mathrm{K}$ is the kinetic energy, $\mathrm{\psi }$ is the work function.

$\Rightarrow \frac{\mathrm{hc}}{{\mathrm{\lambda }}_1}={\mathrm{K}}_1+\mathrm{\psi }$

$\Rightarrow \frac{\mathrm{hc}}{{\mathrm{\lambda }}_2}={\mathrm{K}}_2+\mathrm{\psi }$

$\Rightarrow {\mathrm{K}}_1{\mathrm{\lambda }}_1+{\mathrm{\psi \lambda }}_1={\mathrm{K}}_2{\mathrm{\lambda }}_2+{\mathrm{\psi \lambda }}_2$

$\Rightarrow \mathrm{\psi }=\frac{{\mathrm{K}}_1{\mathrm{\lambda }}_1-{\mathrm{K}}_2{\mathrm{\lambda }}_2}{{\mathrm{\lambda }}_2-{\mathrm{\lambda }}_1}$