A convex lens of focal length 10cm is placed 30 cm in front of a second convex lens also of th esame focal length. A plane mirror is placed after the two lenses. Where should a point object be placed in front of the first lens so that it imagees on to itself?

Explanation

To solve the problem step by step, we need to determine where a point object should be placed in front of the first convex lens so that the image formed by the system (two lenses and a plane mirror) appears at the same location as the object.

### Step 1: Understand the System
We have two convex lenses with a focal length \( f = 10 \, \text{cm} \) each, separated by a distance of \( d = 30 \, \text{cm} \). A plane mirror is placed after the second lens. We need to find the object distance \( u_1 \) for the first lens such that the final image coincides with the object.

### Step 2: Determine the Image Position from the First Lens
The image formed by the first lens will act as the object for the second lens. According to the lens formula:
\[
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