Ray Optics and Optical Instruments - Result Question 30

30. A plano convex lens fits exactly into a plano concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices $\mu_1$ and $\mu_2$ and $R$ is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is

[2013]

(a) $\frac{R}{2(\mu_1-\mu_2)}$

(b) $\frac{R}{(\mu_1-\mu_2)}$

(c) $\frac{2 R}{(\mu_2-\mu_1)}$

(d) $\frac{R}{2(\mu_1+\mu_2)}$

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Answer:

Correct Answer: 30. (b)

Solution:

  1. (b) From the question,

Plano-convex Plano-concave

$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}$

$=(\mu_1-1)(\frac{1}{\infty}-\frac{1}{-R})+(\mu_2-1)(\frac{1}{\infty}-\frac{1}{R})$

$=\frac{(\mu_1-1)}{R}-\frac{(\mu_2-1)}{R} \Rightarrow \frac{1}{f}=\frac{\mu_1-\mu_2}{R}$

$\Rightarrow f=\frac{R}{\mu_1-\mu_2}$ Hence, focal length of the combination is

$\frac{R}{\mu_1-\mu_2}$.