Let the focal lengths of the two lenses be \\\\(f_1\\\\) and \\\\(f_2\\\\).\\\\(u_1 = OC_1\\\\) and \\\\(v_1 = I_1C_1\\\\)\\\\(u_2= -C_1I_1\\\\) which is approximately equal to \\\\(C_2 I_1\\\\) and \\\\(v_2 = C_2I\\\\) which is approximately equal to \\\\(C_1I\\\\) \\\\(\ herefore \\frac{1}{u_1} + \\frac{1}{v_1} = \\frac{1}{f_1}\\\\) and \\\\( \\frac{1}{u_2} + \\frac{1}{v_2} = \\frac{1}{f_2}\\\\) \\\\(\\frac{1}{OC_1} + \\frac{1}{I_1C_1} = \\frac{1}{f1}\\\\) and\\\\(\\frac {1}{- C_1I_1} + \\frac{1}{C_1I} = \\frac{1}{f_2}\\\\)So \\\\(\\frac{1}{OC_1} + \\frac{1}{I_1C_1} = \\frac{1}{f_1} + \\frac{1}{f_2} = \\frac{1}{F}\\\\).Combined focal length of two thin lenses in contact is given by:\\\\(F=\\frac{f_1f_2}{f_1+f_2}\\\\)