One side of radius of curvature `R_2=120 cm` of a convexo-convex lens of material of refractive index `mu=1.5` and focal length `f_1=40 cm` is slivered. It is placed on a horizontal surface with silvered surface in contact with it. Another convex lens of focal length `f_2=20 cm` is fixed coaxially `d=10 cm` above the first lens. A luminous point object O on the axis gives rise to an image coincide with it. Find its height above the upper lens.

Answer

`(100)/(19)` cm

Explanation

`(1)/(f) = (1)/(f_(1)) + (1)/(f_(2)) - (d)/(f_(1)f_(2)) = (2)/(f_(L)) + (1)/(f_(m)) = (2)/(20) + (2)/(120)`
`f_(2) = (120)/(14) = (60)/(7)`
`(1)/(v) - (1)/(u) = (1)/(f) implies (1)/(120) - (1)/(u) = (1)/(20) implies u = (120)/(7)`
`((120)/(7) - 10 = (-50)/(7)) implies (7)/(50) + (1)/(u) = (1)/(20) therefore u = (100)/(19) cm`