A convex lens of focal length `15 cm`, and a concave mirror of radius of curvature `20 cm` are placed co-axially `10 cm` apart. An object is placed in front of convex lens so that there is no parallax between the object and its image formed by the combination. Find the position of the object.

Answer

At 30 cm from lens.

Explanation

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 br 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 happen, rays refracted from convex lens `L` must tend 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 `30 cm` in front of convex lens.
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