An arrow 2.5 cm high is placed at a distance of 25 cm from a diverging mirror of a focal length of 20 cm. Find the nature, position, and size of the image formed.

Step 2: Formula used

The formula 1/f = 1/v + 1/u, where v is the distance between the mirror and the image and u is the distance between the mirror and the object, determines the focal length of the mirror. This is known as the mirror formula.

The formula m = h2/h1 = -v/u, where h2 is the height of the image, h1 is the height of the object, v is the distance of the image from the mirror, and u is the distance of the object from the mirror, yields the magnification.

Step 3: Now we have to find the distance between the image and the object using the mirror formula.

1/20 = 1/v – 1/25

On rearranging we get:

1/v = 1/20 + 1/25

On simplifying we get:

1/v = 9/100

v = 11.11 cm

Step 4: Now we have to find the height of the image

m = h2/h1 = -v/u

h2/2.5 = -11.11/-25

On rearranging we get:

h2 = +1.11 cm

Hence, the image will be formed 11.11 cm behind the mirror, which will be virtual, erect, and 1.11 cm in size.

Summary:

An arrow 2.5 cm high is placed at a distance of 25 cm from a diverging mirror of a focal length of 20 cm. Find the nature, position, and size of the image formed.

An arrow 2.5 cm high is placed at a distance of 25 cm from a diverging mirror of a focal length of 20 cm. The image will be formed at 11.11 cm behind the mirror, which will be virtual, erect, and 1.11 cm in size.