Two media each of refractive index `1.5` with plane parallel boundaries are separated by `100 cm`. `A` convex lens of focal length `60 cm` is placed midway between them with its principal axis normal to the boundaries. `A` luminous point object `O` is placed in one medium on the lens at a distance `125 cm` from it. Find the position of its image formed as a result of refraction through the system.

Answer

`200 cm`, right of the lens

Explanation

`I^(st)` refraction
`(n_(2))/(v)-(n_(1))/(u)=(n_(2)-n_(1))/(R), (1)/(v)-(1.5)/((-75))=(1-1.5)/(infty)=0`
`(1)/(v)=-(1.5)/(75) v=-50 cm`
`u'=-50-50=-100 cm` Object for second refraction.
`(1)/(v)-(1)/(u)=(1)/(f)`
`(1)/(v)-(1)/(100)=(1)/(60) (1)/(v)=(1)/(60)-(1)/(100)`
`v=6xx25=150 cm`
`v=150 cm`
`|||^(rd)` Refraction
`u=150-50=100`
`(n_(2))/(v)-(n_(1))/(u)=(n_(2)-n_(1))/(R) , (1.5)/(v)-(1)/(100)=0 rArr (1.5)/(v) =(1)/(100)`
`v=150 cm` from last surface `v=150 cm`
so from lens `=50+150=200 cm`