Question 315: Ray Optics

Question

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.

Accepted Answer

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

Ray Optics

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.

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