question_answer

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                                [NEET 2013]

A)  \[\frac{R}{2({{\mu }_{1}}+{{\mu }_{2}})}\]   

B)       \[\frac{R}{2({{\mu }_{1}}-{{\mu }_{2}})}\]

C)  \[\frac{R}{({{\mu }_{1}}-{{\mu }_{2}})}\]       

D)       \[\frac{2R}{({{\mu }_{2}}-{{\mu }_{1}})}\]

Correct Answer: C

Solution :

Focal length of the combination

(i)

We have  and

or

or

Putting these values in Eq. (i), we get