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# A system of lenses is formed by fitting a plans convex lens, whose radius of curvature is R and $\mu_1$,the refractive index of plano convex lens is $\large\frac{3}{2}$ and $\mu_2$ the refractive index of Plano concave lens is $\large\frac{4}{3}$. Then the focal length of combination is

$(a)\;2R \\ (b)\;\frac{R}{2} \\ (c)\;6R \\ (d)\;\frac{R}{6}$

For a Plano convex lens
$\large\frac{1}{f_1}=(\mu_1-1) \bigg[ \large\frac{1}{\infty} -\frac{1}{-R}\bigg]$
$\large\frac{1}{f_2}=(\mu_2-1) \bigg[ \large\frac{1}{-R} -\frac{1}{\infty}\bigg]$
For the combination of lens
$\large\frac{1}{F}=\frac{1}{f_1} +\frac{1}{f_2}$
$\qquad= \large\frac{\mu_1 -\mu_2}{R}$
$F= \large\frac{R}{\mu_1 -\mu_2}$
$\quad= \large\frac{R}{\Large\frac{3}{2}-\frac{4}{3} }$
$\quad = \large\frac{R}{\large\frac{1}{6} }$
$F= 6R$
Hence c is the correct answer.