**Convex Lens and Focal Length**

A convex lens is a lens that is thicker in the middle and thinner at the edges. It is also known as a converging lens because it converges the incoming light rays to a point after refraction. The focal length of a lens is the distance between the lens and the point where parallel rays of light converge or appear to converge after passing through the lens.

**Real Image of Same Size as the Object**

In this case, we have a convex lens with a focal length of 8cm that forms a real image of the same size as the object. This implies that the image is formed on the other side of the lens and is inverted compared to the object.

To find the distance between the object and its image, we can use the lens formula:

1/f = 1/v - 1/u

where:
- f is the focal length of the lens
- v is the distance of the image from the lens (positive if the image is on the opposite side of the lens as the object)
- u is the distance of the object from the lens (positive if the object is on the same side of the lens as the incident light)

Since the image formed is real and of the same size as the object, we can consider the magnification (m) to be -1. This implies that the image is inverted.

**Using the Lens Formula**

Substituting the given values into the lens formula, we have:

1/8 = 1/v - 1/u

Since the image is of the same size as the object, the magnification is -1. Therefore, we can write:

m = -v/u = -1

Rearranging the equation, we have:

v = -u

Substituting this back into the lens formula, we have:

1/8 = 1/-u - 1/u

Simplifying the equation, we get:

1/8 = -2/u

Cross-multiplying, we have:

u = -16 cm

Since the object distance (u) is negative, it means that the object is placed on the same side of the lens as the incident light. Therefore, the distance between the object and its image is 16 cm.

Hence, the distance between the object and its image is 16 cm.

We know that image of same size will form if object is placed on centre of curvature. R=2f ,so R=16 so the distance between object and image will be 32 because distance bet object and mirror is 16 and from mirror to image is also 16 so distance between object and image will be 32.