Single Choice

A plano-convex lens (focal length $$f_2$$, refractive index $$\mu_2$$, radius of curvature $$R$$) fits exactly into a plano-concave lens (focal length $$f_1$$, refractive index $$\mu_1$$, radius of curvature $$R$$). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be :

A$$f_1 - f_2$$
B$$f_1 + f_2$$
C$$\dfrac{R}{\mu_2 - \mu_1}$$
Correct Answer
D$$\dfrac{2f_1f_2}{f_1 + f_2}$$

Solution

$$\dfrac{1}{F} = \dfrac{1}{f_1} + \dfrac{1}{f_2} = \dfrac{1 - \mu_1}{R} + \dfrac{\mu_2 - 1}{R}$$

$$\dfrac1F=\dfrac{1-\mu_1+\mu_2-1}{R}=\dfrac{\mu_2-\mu_1}{R}$$

$$F=\dfrac{R}{\mu_2-\mu_1}$$
Option C

SIMILAR QUESTIONS

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