An object is placed 11 cm in front of a convex mirror of focal length 4 cm. Using the lens equation, find where the image will form and state whether it is a real or virtual image.

To find the location and nature (real or virtual) of the image formed by a convex mirror, we can use the lens equation:

1/f = 1/di + 1/do

Where:
- f is the focal length of the mirror
- di is the image distance (distance between the mirror and the image)
- do is the object distance (distance between the mirror and the object)

In this problem, the object distance (do) is 11 cm and the focal length (f) is 4 cm.

Plugging these values into the lens equation, we get:

1/4 = 1/di + 1/11

To solve for di, we need to rearrange the equation:

1/di = 1/4 - 1/11

Now, let's find the common denominator:

1/di = (11 - 4) / (4 * 11)
= 7 / 44

Inverting both sides of the equation:

di = 44 / 7

Simplifying, we find:

di ≈ 6.29 cm

The image distance (di) represents the distance between the mirror and the image. Since the image distance is positive, the image is formed on the opposite side of the mirror compared to the object. Therefore, the image is formed approximately 6.29 cm behind the convex mirror.

Now, to determine the nature of the image, we consider the sign of the image distance. Since the image distance is positive, the image is formed on the opposite side of the mirror. In the case of a convex mirror, the image formed is always virtual and upright. Therefore, the image formed by this convex mirror is virtual.