Solution:

Given, the focal length of a concave mirror, f = -20 cm
The distance of the real image from the mirror, v = -40 cm (negative sign indicates that the image is formed on the same side as the object)

To find: the position of an object

Formula used:

The mirror formula is given as:

1/f = 1/v + 1/u

Where,
f = focal length of the mirror
v = distance of the image from the mirror
u = distance of the object from the mirror

Calculation:

Substitute the given values in the mirror formula, we get:

1/-20 = 1/-40 + 1/u

Simplify the equation, we get:

1/u = 1/-20 - 1/-40

1/u = -1/40

u = -40 cm

Therefore, the position of the object is u = -40 cm.

Explanation:

- The given problem is related to the concave mirror.
- The focal length of the mirror is given as -20 cm, which indicates that the mirror is a concave mirror.
- The distance of the real image from the mirror is given as -40 cm, which means that the image is formed on the same side as the object.
- To find the position of the object, we use the mirror formula, which is given as 1/f = 1/v + 1/u, where f is the focal length of the mirror, v is the distance of the image from the mirror, and u is the distance of the object from the mirror.
- Substitute the given values in the mirror formula, and we get the value of u as -40 cm.
- Therefore, the position of the object is u = -40 cm, which means that the object is located at a distance of 40 cm from the mirror on the same side as the real image.