A plano-convex lens fits exactly into a plano-concave lens. Their surfaces are parallel to each other if the lenses are made of different materials. Will the combination act as a lens? If so, what is its focal length? Is it convergent or divergent ?

Explanation

Let R be the radius of curvature
`(1)/(f_(1)) = - ((n_(1) - 1))/(R) and " " (1)/(f_(2)) = - ((n_(2) - 1))/(R)`
`therefore (1)/(f) = (1)/(f_(1)) + (1)/(f_(2)) = (n_(2) - n_(1))/(R) ne 0 " " because n_(2) ne n_(1)`
Since F has finite value, The combination acts as a lens, It will be conversent if `n_(2) gt n_(1)` and divergent if `n_(2) lt n_(1)`