Here's the solution to the problem:

Given:

• Object height, h = 5 cm
• Object distance, u = -15 cm (negative as per sign convention)
• Focal length, f = -10 cm (negative for concave mirror)

To find:

• Image distance, v
• Image height, h'

Solution:

We can use the mirror formula to find the image distance:

1/f = 1/v + 1/u

Substituting the given values:

1/(-10) = 1/v + 1/(-15)

-1/10 = 1/v - 1/15

1/v = -1/10 + 1/15

1/v = (-3 + 2)/30

1/v = -1/30

v = -30 cm

The screen should be placed 30 cm in front of the mirror to obtain a focused image.

Now, we can use the magnification formula to find the height of the image:

Magnification, m = h'/h = -v/u

Substituting the known values:

h'/5 = -(-30)/(-15)

h'/5 = 30/-15

h'/5 = -2

h' = -10 cm

The height of the image is 10 cm. The negative sign indicates that the image is inverted.

Answer:

• The screen should be placed 30 cm away from the mirror.
• The height of the image is 10 cm. The image is inverted.

Note: These calculations follow the sign conventions used in optics.