A convex lens of focal length 20cm is placed coaxilly with a convex mirror of radius of curvature 20 cm. The two are kept 15 cm apart. A point object is placed 40 cm in front of the convex lens. Find the position of the image formed by this combination. Draw the ray diagram showing the image formation.

Explanation

To solve the problem step by step, we will analyze the system consisting of a convex lens and a convex mirror. We will use the lens formula and the mirror formula to find the position of the final image.

### Step 1: Identify the given data
- Focal length of the convex lens, \( f_1 = +20 \, \text{cm} \)
- Radius of curvature of the convex mirror, \( R = +20 \, \text{cm} \)
- Focal length of the convex mirror, \( f_2 = \frac{R}{2} = +10 \, \text{cm} \)
- Distance between the lens and the mirror, \( d = 15 \, \text{cm} \)
- Object distance from the lens, \( u = -40 \, \text{cm} \) (negative as per sign convention)
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