Question:

A concave mirror has a focal length of 10 cm. An object is placed 20 cm in front of the mirror. Determine the position and nature of the image formed by the mirror.

Answer:

Given:

Focal length (f) = -10 cm (negative sign denotes concave mirror) Object distance (do) = -20 cm (negative sign denotes object placed in front of the mirror)

To find the position of the image (di) and its nature (real or virtual), we can use the mirror equation:

1/f = 1/do + 1/di

Plugging in the known values:

1/-10 = 1/-20 + 1/di

Simplifying the equation:

-1/10 = -1/20 + 1/di

-1/10 = (-1 + 2)/20 + 1/di

-1/10 = 1/20 + 1/di

Now, let's solve for 1/di:

-1/10 - 1/20 = 1/di

(-2 - 1)/20 = 1/di

-3/20 = 1/di

Cross multiplying:

-3di = 20

di = -20/3 cm

The position of the image (di) is approximately -6.67 cm. The negative sign denotes that the image is formed on the same side as the object (in front of the mirror).

To determine the nature of the image, we can use the magnification equation:

magnification (m) = -di/do

Plugging in the values:

m = -(-20/3)/(-20)

m ≈ 1/3

The positive magnification value indicates an upright orientation of the image, and since the magnification value is less than 1, the image is diminished in size. Thus, the nature of the image is a virtual, diminished, and upright image.

In summary, the image is formed approximately 6.67 cm in front of the mirror, and it is virtual, diminished, and upright.