Answer:

To find the nature and size of the image formed by a convex lens, we can use the lens formula:

\(\frac{1}{f} = \frac{1}{v} - \frac{1}{u}\)

Where:

- \(f\) is the focal length of the lens (given as 10 cm).

- \(v\) is the distance of the image from the lens.

- \(u\) is the distance of the object from the lens.

Given that the object's height (h) is 20 meters, we need to convert it to centimeters (1 meter = 100 cm), so h = 2000 cm.

Also, the object distance (u) is given as 15 cm.

Let's plug these values into the lens formula and solve for \(v\):

\(\frac{1}{10} = \frac{1}{v} - \frac{1}{15}\)

Now, solve for \(v\):

\(\frac{1}{v} = \frac{1}{10} + \frac{1}{15}\)

\(\frac{1}{v} = \frac{3 + 2}{30}\)

\(\frac{1}{v} = \frac{5}{30}\)

\(\frac{1}{v} = \frac{1}{6}\)

Now, take the reciprocal of both sides to find \(v\):

\(v = 6\) cm

So, the distance of the image from the lens is 6 cm. Since the image distance is positive, the image is formed on the same side as the object, which means it's a real image.

To find the size of the image, we can use the magnification formula:

\(m = -\frac{v}{u}\)

Where:

- \(m\) is the magnification.

- \(v\) is the image distance (6 cm).

- \(u\) is the object distance (15 cm).

Now, calculate the magnification:

\(m = -\frac{6}{15} = -\frac{2}{5}\)

The negative sign indicates that the image is inverted compared to the object. To find the size of the image, multiply the magnification by the height of the object:

Size of the image = \(m \times \text{height of the object}\)

Size of the image = \(-\frac{2}{5} \times 2000\) cm

Size of the image = -800 cm

Since the size is negative, it means the image is inverted compared to the object, and its height is 800 cm.