Two identical thin biconvex lens of focal length 15 cm and refractive index 1.5 are in contact with each other. The space between the lenses is filled with a liquid of refractive index 1.25. The focal length of the combination is __________ cm.

<p>$${1 \over {{f_l}}} = \left( {{{{\mu _e}} \over {{\mu _m}}} - 1} \right)\left( {{1 \over {{R_1}}} - {1 \over {{R_2}}}} \right)$$</p> <p>here $|{R_1}| = |{R_2}| = R$</p> <p>$$ \Rightarrow {1 \over {{f_{{l_1}}}}} = (1.5 - 1)\left( {{2 \over R}} \right) = {1 \over {15}}$$</p> <p>$\Rightarrow {1 \over R} = {1 \over {15}}$ or $R = 15$ cm</p> <p>for the concave lens made up of liquid</p> <p>$${1 \over {{f_{{l_2}}}}} = (1.25 - 1)\left( { - {2 \over R}} \right) = - {1 \over {30}}$$ cm</p> <p>now for equivalent lens</p> <p>${1 \over {{f_e}}} = {2 \over {{f_{{l_1}}}}} + {1 \over {{f_{{l_2}}}}}$</p> <p>$= {2 \over {15}} - {1 \over {30}} = {3 \over {30}} = {1 \over {10}}$</p> <p>or ${f_e} = 10$ cm</p>