**Max Focal Length of a Convex Lens for Real Image Formation**

To determine the maximum focal length of a convex lens that can form a real image on a screen at a given distance from an object, we need to consider the properties of the convex lens and the formation of real images.

**Formation of Real Images by Convex Lens:**
A convex lens is a converging lens that can form both real and virtual images. When an object is placed in front of a convex lens, the lens refracts the light rays coming from the object and converges them to form an image. The image formed can either be real or virtual, depending on the position of the object and the lens.

**Real Image Formation:**
A real image is formed when the light rays converge to a point after passing through the lens. It can be projected onto a screen and is always formed on the opposite side of the lens from the object. Real images are always inverted and can be larger or smaller than the object, depending on the distance between the object and the lens.

**Determination of Maximum Focal Length:**
In order for a real image to be formed on a screen at a distance of 80cm from the object, we need to consider the lens formula:

1/f = 1/v - 1/u

where f is the focal length of the lens, v is the image distance, and u is the object distance. We can rearrange the formula to solve for the focal length:

f = 1 / (1/v - 1/u)

Assuming the object distance (u) is positive and the image distance (v) is negative for a real image, we can substitute the given values:

f = 1 / (1/-80 - 1/u)

To determine the maximum focal length, we need to consider the limiting case when the image distance (v) is at its maximum negative value, which means the image is formed at the focal point of the lens. In this case, v = -f. Substituting this into the formula:

f = 1 / (1/-80 - 1/u)
f = 1 / (-1/80 - 1/u)

To maximize the focal length, we need to minimize the denominator. This can be achieved when the object distance (u) is very close to infinity, which means the object is placed at an extremely large distance from the lens. In this case, we can approximate the formula as:

f = 1 / (-1/80 - 0)
f = -80 cm

Therefore, the maximum focal length of the convex lens should be -80 cm.