A convex lens of focal length `20 cm` is placed co-axially with a convex mirrir of radius of curvature `20 cm`. The two are kept `15 cm` apart from eachother. A point object is placed `60 cm` in front of the convex lens. Find the position of the image formed by the combination.

Explanation

The set up ia shown in Fig.
For the convex lens, `f = 20 cm ,`
`u = OC = -60 cm`
As `(1)/(v)-(1)/(u)=(1)/(f)`
`:. (1)/(v)=(1)/(f)+(1)/(u)=(1)/(20)-(1)/(60)=(3 - 1)/(60)=(2)/(60)`
`v = (60)/(2) = 30 cm`
If image by lens alone is formed at `I_1`. then `C I_1 = 30 cm`
For the convex mirror, `I_1` acts as a virtual object.
Therefore, `u = PI_1 = CI_1 = 30 - 15 = 15 cm`,
`R = 20 cm, v = ?`
From
`(1)/(v)+(1)/(u)=(2)/( R) (1)/(v)=(2)/( R)-(1)/(u)=(2)/(20)-(1)/(15) = (1)/(30)`
`v = 30 cm`
`:.` Final image by the combination is formed at `I`, where `PI = 30 cm`.
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