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A convex lens (of focal length 20 cm) an...

A convex lens (of focal length 20 cm) and a concave mirror, having their principal axes align the same lines, are kept 80 cm apart from each other. The concave mirror is to the right of the convex lens. When an object is kept at a distance of 30 cm to the left of the convex lens, its image remains at the same position even if the concave mirror is removed. The maximum distance (in cm) of the object for which this concave mirror, by itself would produce a virtual image would be:

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To solve the problem, we need to analyze the situation step by step. ### Step 1: Understand the setup We have a convex lens with a focal length \( f_L = 20 \) cm and a concave mirror. The distance between the lens and the mirror is \( d = 80 \) cm. The object is placed \( 30 \) cm to the left of the convex lens. ### Step 2: Find the image formed by the convex lens Using the lens formula: \[ ...
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