Introduction When an object is placed in front of a mirror, an image is formed due to the reflection of light. The size and position of the image depend on the type of mirror and the distance of the object from the mirror.

Given - Focal length of the mirror, f = 20 cm - Size of the image is 1/3rd of the size of the object

Calculations Let the distance of the object from the mirror be u and the size of the object be h.

Using the mirror formula, 1/f = 1/u + 1/v, where v is the distance of the image from the mirror, we can find the distance of the image from the mirror.

As the image is reduced to 1/3rd of the size of the object, the height of the image, h' = h/3.

Using the magnification formula, m = h'/h = -v/u, we can find the distance of the object from the mirror.

Solution - Using the magnification formula, m = h'/h = -v/u, we get m = -1/3

- As the magnification is negative, the image is inverted.

- Using the mirror formula, 1/f = 1/u + 1/v, and substituting the values, we get 1/20 = 1/u + 1/v

- Using the magnification formula, m = -v/u, and substituting the values, we get -1/3 = -v/u

Solving these two equations, we get u = 15 cm v = -45 cm (negative sign indicates that the image is inverted)

- Therefore, the object has been placed at a distance of 15 cm from the mirror.

- As the image is inverted and real, the mirror is a concave mirror.

Conclusion In conclusion, the object has been placed at a distance of 15 cm from the concave mirror having a focal length of 20 cm. The image formed is inverted and real, and its distance from the mirror is -45 cm. Thus, the mirror is a concave mirror.