A convex lens of focal length `20 cm` and a convex mirror of focal length `10 cm` are placed co-axially `50 cm` apart from each other. An incident beam parallel to its principal axis is incideent on the convex lens. Locate the position of final image formed due to the combination.

Explanation

The set up is shown in Fig. When the beam incident on convex lens is parallel to principal axis of the lens, on refraction, it collects at focus of the lens forming the image `I_1`, where `CI_1 = F = 20 cm. I_1` acts as a real object for concave mirror, whose real image is formed at `I`. We have to find `PI = v = ?` For the concave mirror,
`u = PI_1 = CP - CI_1 = 50 - 20 = (-) 30 cm`,
`f =-10 cm`
From
`(1)/(v)+(1)/(u)=(1)/(f),(1)/(v)=(1)/(f)-(1)/(u)=(1)/(-10)+(1)/(30)= -(1)/(15)`
Negative sign indicates that final image at `i` is real.
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