Question

Two identical thin biconvex lenses 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.

Answer 1

$\frac{1}{f_1}$=($\frac{μ_e}{μ_{m-1}}$)($\frac{1}{R_1}-\frac{1}{R_2}$)
here |R1|=|R2|=R
⇒$\frac{1}{fl_1}$=(1.5-1)(-$\frac{2}{R}$)=$\frac{1}{15}$
⇒$\frac{1}{R_1}$=$\frac{1}{15}$ or R=15 cm
for the concave lens made up of liquid
⇒$\frac{1}{fl_2}$=(1.25-1)(-$\frac{2}{R}$)=-$\frac{1}{30}$ cm
now for an equivalent lens,
$\frac{1}{f_e}$=$\frac{2}{fl_1}$+$\frac{1}{fl_2}$
=$\frac{2}{15}$-$\frac{1}{30}$=$\frac{3}{30}$=$\frac{1}{10}$
or f e = 10 cm