Q. A plano convex lens of refractive index $\mu_1$ and focal length $f_1$ is kept in contact with another plano concave lens of refractive index $\mu_2$ and focal length $f_2$. If the radius of curvature of their spherical faces is R each and $f_1 = 2f_2$, then $\mu_1$ and $\mu_2$ are related as :

Solution:

$\frac{1}{2f_{2}} = \frac{1}{f_{1}} =\left(\mu_{1} -1\right)\left(\frac{1}{\infty} - \frac{1}{-R}\right) $
$ \frac{1}{f_{2}} = \left(\mu_{2} -1\right) \left(\frac{1}{-R} - \frac{1}{\infty}\right) $
$ \frac{\left(\mu_{1}-1\right)}{R} = \frac{\left(\mu_{2}-1\right)}{2R} $
$2\mu_{2} -\mu_{2} = 1 $

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