Correct Answer - At `30 cm` from lens
The given set up is shown in Fig. Here, focal length of lens, `f = 15 cm` , radius of curvature of concave mirror, `R = 20 cm` and `CP = 10 cm`. Let the object be at `O`, where `CO = u`. As there is no parallax between the object and its image formed by the combination, therefore, final image must be at `O` itself. For this to happens, rays refracted from convex lens `L` must tens to meet at `I_(1)`, the centre of curvature of concave mirror. These rays would fall normally on concave mirror and retrace their path on reflection.
`:. PI_(1) = R = 20 cm`.
For the lens,
`v = CI_(1) = CP + PI_(1) = 10 + 20 = 30 cm`.
From `(1)/(v) - (1)/(u) = (1)/(f)`
`-(1)/(u) = (1)/(f) - (1)/(v) = (1)/(15) - (1)/(30) = (1)/(30)`
`:. u = - 30 cm`, i.e., `CO = 30 cm`
i.e., object must be at `30cm` in front of convex lens.