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  4. A plano convex lens of refractive index μ1 and focal length f1 is kept in contact with another plano concave lens of refractive index μ2 and focal length f2. If the radius of curvature of their spherical faces is R each and f1 = 2f2, then μ1 and μ2 are related as :

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 :

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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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