A convex lens is placed between an object and a screen which are at a fixed distance apart for one position of the lens. The magnification of the image obtained on the screen is `m_(1)`. When the lens is moved by a distance d the magnification of the image obtained on the same screen `m_(2)`, Find the focal length of the lens.

Explanation

To find the focal length of the convex lens when it is moved between a fixed object and screen, we can follow these steps:

### Step 1: Understand the Setup
We have a convex lens placed between an object and a screen. The distance between the object and the screen is constant, denoted as \( D \). The lens is moved by a distance \( d \), resulting in two different magnifications \( m_1 \) and \( m_2 \).

### Step 2: Define the Relationships
When the lens is in position 1, let:
- \( u_1 \) = object distance from the lens
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