The Problem:
A convex mirror has a radius of curvature of 22 cm. An object is placed 14 cm away from the mirror. We need to determine the position and nature of the image formed by the mirror.

Solution:

Step 1: Identify the Given Information:
- Radius of curvature (R) = 22 cm
- Object distance (u) = -14 cm (negative sign indicates the object is placed on the same side as the observer)

Step 2: Determine the Focal Length:
The focal length (f) of a convex mirror is half of its radius of curvature. Therefore, in this case, the focal length can be calculated as:
f = R/2 = 22 cm / 2 = 11 cm

Step 3: Apply the Mirror Formula:
The mirror formula is given by:
1/f = 1/v - 1/u

Where:
- f is the focal length
- v is the image distance (positive for a virtual image and negative for a real image)
- u is the object distance

Rearranging the formula, we get:
1/v = 1/f + 1/u

Step 4: Calculate the Image Distance:
Substituting the given values into the formula, we have:
1/v = 1/11 cm + 1/-14 cm

Simplifying the equation, we get:
1/v = (-14 + 11) / (11 * -14)
1/v = -3 / (-154)
1/v = 1/51

Taking the reciprocal of both sides, we find:
v = 51 cm

Step 5: Analyze the Image:
The positive value of v indicates that the image is formed on the same side as the observer, which means it is a virtual image.

Step 6: Determine the Image Position:
The image distance (v) is positive, indicating that the image is formed on the same side as the observer. Therefore, the image is formed at a distance of 51 cm from the convex mirror.

Conclusion:
The image formed by the convex mirror, with a radius of curvature of 22 cm, when an object is placed 14 cm away from it, is a virtual image located 51 cm away from the mirror.

154/18