Given:
focal length, f = -20cm
Magnification, m = -3 (since virtual image)

To find:
Object distance, u

Solution:

Magnification formula is given as:

m = -v/u

where,
v = image distance (negative for virtual image)
u = object distance (positive for real object)

Substituting the given values, we get:

-3 = -v/u

Multiplying both sides by -1, we get:

3 = v/u

Using mirror formula, we get:

1/f = 1/u + 1/v

Substituting the given values, we get:

1/-20 = 1/u + 1/v

Rearranging the terms, we get:

1/v = 1/-20 - 1/u

Substituting v = 3u, we get:

1/3u = 1/-20 - 1/u

Multiplying both sides by 3u, we get:

1 = -3u/-20 + 3

Simplifying, we get:

u = 15 cm

Therefore, the object distance is 15 cm.

Explanation:

- Magnification formula is used to relate the size of the image with the size of the object.
- Mirror formula is used to relate the object distance, image distance and focal length of the mirror.
- We are given the magnification of the image, which helps us to relate the object distance and image distance.
- Substituting the given values in the equation and simplifying gives us the object distance.
- The negative sign in the focal length indicates that the mirror is concave.
- The virtual image is formed behind the mirror and is upright, which means it is a magnified image of the object.