Size of the image of an object by a mirror having a focal length of 20 cm is observed to be reduced to 1/3rd of its size. At what distance has the object been placed from the mirror? What is the nature of the image and the mirror?

The magnification (m) of a mirror is given by the ratio of the image height to the object height. In this case, the image is reduced to 1/3rd of its size, so m = -1/3 (the negative sign indicates that the image is inverted).

The mirror formula, which relates the object distance (u), the image distance (v), and the focal length (f) of the mirror, is given by 1/f = 1/v + 1/u.

The magnification is also equal to the ratio of the image distance to the object distance, or m = -v/u.

We can use these two equations to solve for the object distance.

First, substitute m = -v/u into the mirror formula:

1/f = 1/v + 1/u 1/f = 1/v - m/v 1/f = (1-m)/v

Rearrange to solve for v:

v = (1-m)/f v = (1-(-1/3))/20 cm v = 4/3 * 20 cm v = 80/3 cm

Then, substitute v back into the equation m = -v/u to solve for u:

-1/3 = -80/3u u = 80 cm

So, the object has been placed 80 cm from the mirror.

The negative magnification indicates that the image is inverted, which is a characteristic of real images. Real images are formed by converging mirrors, so the mirror is a concave mirror.

The magnification (m) of a mirror is given by the ratio of the image height to the object height. In this case, the image is reduced to 1/3rd of its size, so m = -1/3 (the negative sign indicates that the image is inverted).

The mirror formula is given by 1/f = 1/v + 1/u, where f is the focal length, v is the image distance, and u is the object distance. We also know that the magnification m = -v/u.

We can substitute the second equation into the first to get 1/f = -1/m + 1/u. Rearranging terms gives us u = 1/(1/f + m).

Substituting the given values, we get u = 1/(1/(-20 cm) - 3) = -15 cm.

The negative sign indicates that the object is placed on the same side as the light is coming from, which is typical for mirrors.

The image is inverted and reduced in size, which is characteristic of a real image. The mirror is concave, because it is the only type of mirror that can produce a real, inverted, reduced image.