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

A, C

Explanation

`1/40=(1.5-1)(1/120+1/(R_1))`
Solving we get, `R_2=24 cm`
Applying lens formula, for `L_2`

`1/(v_1)+1/x=1/20……(i)`
Using `(mu_2)/v-(mu_1)/u=(mu_2-mu_1)/R` for unsilvered side of `L_1.`
`1.5/(-120)-1.0/(v_1-10)=(1.5-1.0)/24...(ii)`
Solving Eqs.(i) and (ii), we get `x=10 cm`