Derive the lens formula, `(1)/(2)=(1)/(v)-(1)/(u)` for a concave lens, using the necessary ray diagram.
Two lenses of powers 10 D and -5 D are placed in contact.
(i) Calculate the power of the new lens.
(ii) Where should an object be held from the lens, so as to obtain a virtual image of magnification 2?

Explanation

To derive the lens formula for a concave lens and solve the given problems, let's break it down step by step.

### Step 1: Deriving the Lens Formula for a Concave Lens

1. **Draw the Ray Diagram**:
- Draw a concave lens, which is thinner at the center and thicker at the edges.
- Mark the principal axis, the optical center (O), the focal point (F), and the center of curvature (C).
- Place an object (AB) on the left side of the lens, between the focal point and the lens.
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